algebraic k theory of group rings and the cyclotomic trace map we prove that the farrell jones assembly map for connective alge braic k theory is rationally injective under mild homological niteness condi tions on the group and assuming that a weak version of the leopoldt schneider conjecture holds for cyclotomic elds this generalizes a result of bokstedt hsiang and madsen and leads to a concrete description of a large direct summand of kn z g z q in terms of group homology in many cases the number theoretic conjectures are true so we obtain rational injectivity results about assembly maps in particular for whitehead groups under niteness assumptions on the group only the proof uses the cyclotomic trace map to topological cyclic homology bokstedt hsiang madsen s functor c and new general injectivity results about the assembly maps for topological hochschild homology and c

existence of maximal surfaces in asymptotically flat spacetimes we prove the existence of maximal surfaces in asymptotically flat spacetime satisfying an interior condition this uses a priori estimates which can also be applied to prescribed mean curvature surfaces in cosmological spacetimes and the dirichlet problem

the relationship between frequency selectivity and pitch discrimination sensorineural hearing loss this study tested the relationship between frequency selectivity and the minimum spacing between harmonics necessary for accurate fo discrimination fundamental frequency difference limens fo dls were measured for ten listeners with moderate sensorineural hearing loss snhl and three normal hearing listeners for sine and random phase harmonic complexes bandpass filtered between 1500 and 3500 hz with fo s ranging from 75 to 500 hz or higher all listeners showed a transition between small good fo dls at high fo s and large poor fo dls at low fo s although the fo at which this transition occurred fo tr varied across listeners three measures thought to reflect frequency selectivity were significantly correlated to both the fo tr and the minimum fo dl achieved at high fo s 1 the maximum fo for which fo dls were phase dependent 2 the maximum modulation frequency for which amplitude modulation and quasi frequency modulation were discriminable and 3 the equivalent rectangular bandwidth of the auditory filter estimated using the notched noise method these results provide evidence of a relationship between fo discrimination performance and frequency selectivity in listeners with snhl supporting spectral and spectro temporal theories of pitch perception that rely on sharp tuning in the auditory periphery to accurately extract fo information

local linearization stability it is shown that einstein s equations are always linearization stable around any finite region of space time let g0ab be any region of space time admitting a compact cauchy surface with nonempty smooth boundary and with g0ab a sufficiently smooth solution of the vacuum einstein equation it is shown that for any solution g1ab of the linearized equation and any open region u there exists a smooth one parameter family g ab of solutions on u such that g ab 0 g0ab u and d d g ab g1ab u by using a result of choquet bruhat and york the cauchy problem general relativity and gravitation edited by a held plenum new york 1980 vol 1 asserting the smoothness of the map that sends initial data into solutions of einstein s evolution equations the proof of the above theorem is reduced to the proof of a similar theorem for einstein s constraint equations the proof of this latter theorem involves the use of the implicit function theorem in hilbert spaces this local result on lineariza

frequency resolution and discrimination of constant and dynamic tones in normal and hearing impaired listeners frequency resolution and three tasks of frequency discrimination were measured at 500 and 4000 hz in 12 normal and 12 hearing impaired listeners a three interval two alternative forced choice procedure was used frequency resolution was measured with an abbreviated psychoacoustical tuning curve frequency discrimination was measured for 1 a fixed frequency standard and target 2 a fixed frequency standard and a frequency transition target and 3 frequency transition standard and a frequency transition target the 50 ms frequency transitions had the same final frequency as the standards but the initial frequency was lowered to obtain about 79 discrimination performance there was a strong relationship between poor frequency resolution and elevated pure tone thresholds but only a very weak relationship between poor frequency discrimination and elevated pure tone thresholds several hearing impaired listeners had normal discrimination performance together with pure tone thresholds of 80 90 db hl a slight correlation was found between word recognition and frequency discrimination but a detailed comparison of the phonetic errors and either the frequency discrimination or frequency resolution tasks failed to suggest any consistent interdependencies these results are consistent with previous work that has suggested that frequency resolution and frequency discrimination are independent processes

the farrell hsiang method revisited we present a sufficient condition for groups to satisfy the farrell jones conjecture in algebraic k theory and l theory the condition is formulated in terms of finite quotients of the group in question and is motivated by work of farrell hsiang

the stable topological hyperbolic space form problem for complete manifolds of finite volume about fifteen years ago a borel posed the following conjecture let m be a closed aspherical manifold i e rcim o for i 1 if g n m is a homotopy equivalence where n is another manifold then g is homotopic to a homeomorphism a stable version of this conjecture for m r a closed nonpositively curved manifold was verified in 4 corollary b namely if m is a closed non positively curved manifold and g n m is a homotopy equivalence where n is a manifold then

on bundles that admit fiberwise hyperbolic dynamics this paper is devoted to rigidity of smooth bundles which are equipped with fiberwise geometric or dynamical structure we show that the fiberwise associated sphere bundle to a bundle whose leaves are equipped with continuously varying metrics of negative curvature is a topologically trivial bundle when either the base space is simply connected or more generally when the bundle is fiber homotopically trivial we present two very different proofs of this result a geometric proof and a dynamical proof we also establish a number of rigidity results for bundles which are equipped with fiberwise anosov dynamical systems finally we present several examples which show that our results are sharp in certain ways or illustrate necessity of various assumptions

the k theoretic farrell jones conjecture for hyperbolic groups we prove the k theoretic farrell jones conjecture for hyperbolic groups with twisted coefficients in any associative ring with unit

on the higher whitehead groups of a bieberbach group let t be a bieberbach group i e the fundamental group of a compact flat riemannian manifold in this paper we show that if p 2 is a prime then the p torsion subgroup of wh r vanishes for 0 i 2p 2 where wh r is the th higher whitehead group of t the proof involves farrell and hsiang s structure theorem for bieberbach groups parametrized surgery pseudoisotopy and waldhausen s algebraic if theory of spaces

rigidity and crystallographic groups i this is the first in a series of articles about rigidity theorems for crystallographic groups the main theorem is 1 1 it is an h cobordism rigidity statement it implies see 1 6 that any crystallographic manifold with odd order holonomy which is h cobordant and simply homotopically equivalent to the standard one is actually homeomorphic to it in the second part of this work 9 we will exploit this result to prove that one can remove the word h cobordant from the previous sentence the main theorem concerns an involution on the group wh p mr this is the group of g h cobordisms of the flat torus mr of a crystallographic group f with holonomy group g definitions of these terms appear in 1 4 we prove a vanishing result of the tate cohomology

age related changes in within and between channel gap detection using sinusoidal stimuli pure tone gap stimuli with identical within channel or dissimilar between channel marker frequencies of 1 and 2 khz were presented to young and old listeners in a two interval forced choice gap detection task to estimate the influence of extraneous duration cues on gap detection thresholds in the between channel conditions were obtained for two different sets of reference stimuli reference stimuli that were matched to the overall duration of the gap stimulus i e two markers plus the gap and reference stimuli that were fixed at the combined duration of the two markers excluding the gap results from within channel conditions were consistent with previous studies i e there were small but highly reliable age differences smaller gap thresholds at longer marker durations and an interaction between the two variables in between channel conditions however age differences were not as clear cut rather the effect of age varied as a function of duration cue and was more pronounced when stimuli were matched for overall duration than when the duration of the reference tone was fixed

topological nonrigidity of nonuniform lattices we say that an arbitrary manifold m m is topologically rigid relative to its ends if it satisfies the following condition if n n is any other manifold with a compact subset c n for which a proper homotopy equivalence h n n m m is a homeomorphism on n n c then there is a compact subset k n and a proper homotopy ht n n m m from h to a homeomorphism such that ht and h agree on n n k for all t 0 1 we say that a manifold m without boundary is properly rigid or absolutely topologically rigid if we eliminate the requirements that h be a homeomorphism on n n c and agree with ht on n n k for all t 0 1 along the lines of the classical borel conjecture that all closed aspherical manifolds are topologically rigid farrell and jones 8 provide the following important theorem

pinching constants for hyperbolic manifolds we show in this paper that for everyn 4 there exists a closedn dimensional manifoldv which carries a riemannian metric with negative sectional curvaturek but which admits no metric with constant curvaturek 1 we also estimate the pinching constantsh for which our manifoldsv admit metrics with 1 k h

continuously controlled algebraic k theory of spaces and the novikov conjecture here the l polynomial is a certain rational polynomial in the pontrjagin classes this theorem is surprising from many points of view the left hand side is obviously a homotopy invariant and an integer whereas the right hand side a priory is only a smooth invariant and a rational number this led novikov to the following conjecture if m has fundamental group and x is an element in h b f the classifying map could it be that the higher signatures x l m m are homotopy invariants of the manifold m from this point of view hirzebruch s theorem is a verification of the novikov conjecture for simply connected manifolds later wall 17 section 17h realized that the novikov conjecture can be expressed using the assembly map h b l z l z the novikov conjecture is equivalent to the assembly map being a rational monomorphism over the years it has turned out that there are lots of assembly maps in algebraic ktheory in c theory and in a theory among others it has become common practice to call the statement that the assembly map is a rational monomorphism the novikov conjecture in that theory in the case of c theory monicity of the assembly map implies but is not equivalent to the classical novikov conjecture in this paper we treat the a theory case we wish to extend the results in 6 and 7 to a theory using a variation of the continuously controlled a theory in 13 15 to replace the continuously controlled k theory in 1 one of the main problems here is that as a computational device slightly discontinuous maps were allowed in 1 and 6 and atheory does not respond nicely to that the answer is to work with spaces that are so locally contractible that the slightly discontinuous maps eventually continuous maps can be replaced by continuous maps otherwise the strategy is to follow 7 6 and 13 15 and we shall assume the reader has some familiarity with these papers we prove the following theorem

the farrell jones conjecture for mapping class groups we prove the farrell jones conjecture for mapping class groups the proof uses the masur minsky theory of the large scale geometry of mapping class groups and the geometry of the thick part of teichmuller space the proof is presented in an axiomatic setup extending the projection axioms in bestvina et al publ math inst hautes etudes sci 122 1 64 2015 more specifically we prove that the action of mathrm mod sigma on the thurston compactification of teichmuller space is finitely mathcal f amenable for the family mathcal f consisting of virtual point stabilizers

the role of stimulus complexity spectral overlap and pitch for gap detection thresholds in young and old listeners thresholds for detecting a gap between two complex tones were determined for young listeners with normal hearing and old listeners with mild age related hearing loss the leading tonal marker was always a 20 ms 250 hz complex tone with energy at 250 500 750 and 1000 hz the lagging marker also tonal could differ from the leading marker with respect to fundamental frequency f0 the presence versus absence of energy at f0 and the degree to which it overlapped spectrally with the leading marker all stimuli were presented with steeper 1 ms and less steep 4 ms envelope rise and fall times f0 differences decreases in the degree of spectral overlap between the markers and shallower envelope shape all contributed to increases in gap detection thresholds age differences for gap detection of complex sounds were generally small and constant when gap detection thresholds were measured on a log scale when comparing the results for complex sounds to thresholds obtained for pure tones in a previous study by heinrich and schneider 2006 j acoust soc am 119 2316 2326 thresholds increased in an orderly fashion from markers with identical within channel pure tones to different between channel pure tones to complex sounds this pattern of results was true for listeners of both ages although younger listeners had smaller thresholds overall

k theory and dynamics i un theoreme de h cobordisme avec commande feuillettee la variete associee le transfert asymptotique dynamique du flot geodesique completion de la demonstration du theoreme principal revue de la theorie de la commande structures de longues cellules minces

isomorphism conjectures in algebraic k theory duff in this paper we are concerned with the four functors y y3 if and which map from the category of topological spaces x to the category diff of q spectra the functor 3 or if maps the space x to the qspectrum of stable topological or smooth pseudoisotopies of x the spaces diff dif 3i x id9 x i 0 are hatcher s deloopings of 970 x yd x cf 29 the functor j maps a path connected space x to the algebraic ktheoretic s2 spectrum for the integral group ring z7r1x the spaces x x i 0 are the gersten wagoner deloopings of z o x cf 27 52 5 x is also defined on a nonpath connected space x to be x1 where xi i e i are the path components of x and ii xi indicates the direct limit of all finite products of the i xi i e i if x is path connected then the functor maps x to the l surgery classifying spaces for oriented surgery problems with fundamental group r i1x identified by their fourfold periodicity k 90 x k 4j x cf 35 39 44 47 in addition if x is not path connected then we set y77 x tiei5 fj xi where xi i e i are the path components of x results obtained by the authors over the past five years cf 15 25 and in particular 19 16 a 1 a 18 together with many earlier results and conjectures which are reviewed in 1 6 1 1 6 6 suggest that for any connected cwcomplex x and for 5 denoting any of the above functors the q spectrum x should be computable in a simple way from the values taken by 9 on covering spaces of x which have very simple fundamental groups in more detail we let 9 x denote the collection of all subgroups h c ir ix which are either finite or virtually infinite cyclic a group h is virtually infinite cyclic if there is a short exact sequence of groups 1 z h f 1 with f equal to a finite group and z equal to the infinite cyclic group for each such group we let xh x denote the covering space projection corresponding to h then the q spectrum 5 x should be computable in a simple way from the q spectra 5 xh h e 9 x the purpose of this paper is to formulate precisely a conjecture along these lines and to verify the conjecture for any x

the lifting problem for affine structures in nilpotent lie groups affine manifolds occur in several situations in pure and applied mathematics e g leaves of lagrangian foliations completely integrable hamiltonian systems linear representations of virtually polycyclic groups geometric quantization and so on this work is devoted to left invariant affinely flat structures in lie groups we are mainly concerned with the following situation let g and go be nilpotent lie groups of dimension n 1 and n respectively and let h g p go be a continuous homomorphism from g onto go given a left invariant affinely flat structure go vo the lifting problem is to discover whether g has a left invariant affinely flat structure g v such that h becomes an affine morphism in the present work we answer positively when go vo is normal therefore the existence problem for a left invariant complete affinely flat structure in nilpotent lie groups is solved by applying the following subsequent results let tf go be the set of left invariant affinely flat structures in the nilpotent lie group go 10 tf go 0 implies the existence of normal structure go vo e tf go 20 h g go being as above every normal structure go v0 has a normal lifted in atf g

a pl geometric study of algebraic k theory this paper manages to apply the farrell jones theory on algebraic k groups of closed negatively curved riemannian manifolds to gromov s hyperbolic group theory the paper reaches the conclusion that for any finite polyhedron k with negative curvature wh 1 k 0

dynamic asymptotic dimension relation to dynamics topology coarse geometry and c algebras we introduce dynamic asymptotic dimension a notion of dimension for actions of discrete groups on locally compact spaces and more generally for locally compact etale groupoids we study our notion for minimal actions of the integer group its relation with conditions used by bartels luck and reich in the context of controlled topology and its connections with gromov s theory of asymptotic dimension we also show that dynamic asymptotic dimension gives bounds on the nuclear dimension of winter and zacharias for c algebras associated to dynamical systems dynamic asymptotic dimension also has implications for k theory and manifold topology these will be drawn out in subsequent work

detection of silent temporal gaps in sinusoidal markers gap detection thresholds were measured by forced choice procedure for conditions where the duration of a silent gap was varied adaptively between pairs of sinusoidal markers of the same or different frequency frequencies of the first sinusoid in a pair of markers ranged from f1 500 to 4000 hz second sinusoid marker frequencies f2 included f1 f2 and usually frequencies 2 5 24 and 50 higher than f1 in preliminary studies the role of presentation level e n0 on gap detection was considered preliminary data revealed confounding extraneous factors arising from gating transients and from overall stimulus i e markers gap and or masker duration cues in the main experiments the contributions of these extraneous cues were evaluated with experimental designs aimed at identifying and minimizing the confounding roles of these cues in gap detection for conditions where extraneous gating transient cues were minimized by presenting the sinusoidal markers in a continuous noise masker with random onset phase for the second sinusoid in every pair of markers and overall stimulus duration cues were diminished by randomizing the duration of each marker independently gap detection thresholds increased from 5 to 90 ms as the frequency separation between f1 and f2 was increased by half an octave when the gap detection thresholds were treated as filter attenuation values by normalizing and converting the data into decibels the data were closely fit by the roex filter model on average the listeners performances were modeled well by a constant percentage 7 bandwidth filter centered on f1

gap detection and the precedence effect in young and old adults thresholds for detecting a gap between two gaussian enveloped standard deviation 0 5 ms 2 khz tones were determined in young and old listeners the gap detection thresholds of old adults were more variable and about twice as large as those obtained from young adults moreover gap detection thresholds were not correlated with audiometric thresholds in either group estimates of the width of the temporal window of young subjects based on the detection of a gap between two tone pips were smaller than those typically obtained when a relatively long duration pure tone is interrupted moore et al j acoust soc am 85 1266 1275 1989 because the amount of time it takes to recover from an adapting stimulus is likely to affect gap detection thresholds glasberg et al j acoust soc am 81 1546 1556 1987 smaller estimates of temporal window size would be expected in this paradigm if the amount of adaptation produced by the first tone pip was negligible the larger gap detection thresholds of o

algebraic k theory of discrete subgroups of lie groups abstract let g be a lie group with finitely many connected components and be a discrete cocompact torsion free subgroup of g we rationally calculate the algebraic k theory of the integral group ring z in terms of the homology of with trivial rational coefficients

modular symbols and the topological nonrigidity of arithmetic manifolds in this paper we address the existence of smooth manifolds proper homotopy equivalent to nonuniform arithmetic manifolds m g k that are not homeomorphic to it while the manifolds m are properly rigid if rank 2 we show that the so called virtual structure group has infinite rank as a vector space if rank 4 2015 wiley periodicals inc

structure of manifolds of nonpositive curvature clearly 1 rank m dim m we may regard rank m as a measurement of the flatness of m since a parallel field x along yv and perpendicular to yv is a jacobi field if and only if the sectional curvatures of the planes i t a x t are zero for all t e r in particular m is flat if rank m dim m hence a compact surface of nonpositive curvature has rank one unless it is a torus or a klein bottle it also follows that rank m1 x m2 rank ml rank m2 finally it is important that the definition of rank m above coincides with the usual one if m is locally symmetric

on the farrell jones conjecture for higher algebraic k theory here b is the classifying space of the group and we denote by k r the non connective algebraic k theory spectrum of the ring r the homotopy groups of this spectrum are denoted kn r and coincide with quillen s algebraick groups of r qui73 in positive dimensions and with the negative k groups of bass bas68 in negative dimensions the homotopy groups of the spectrum x k r are denotedhn x k r they yield a generalized homology theory and in particular standard computational tools such as the atiyah hirzebruch spectral sequence apply to the left hand side of the assembly map above as a corollary of the main result of this paper we prove conjecture 1 1 in the case where is the fundamental group of a closed riemannian manifold with strictly negative sectional curvature in fact our result is more general and applies to group rings r where r is a completely arbitrary coefficient ring note that if one replaces in conjecture 1 1 the coefficient ring z by an arbitrary coefficient ringr the corresponding conjecture would be false already in the simplest non trivial case if c is the infinite cyclic group the bass heller swan formula bhs64 gra76 p 236 for kn rc kn r t 1 yields that kn rc kn 1 r kn r nkn r nkn r where nkn r is defined as the cokernel of the split inclusion kn r kn r t and does not vanish in general but since s is a model for bc one obtains on the left hand side of the assembly map only hn bc k r kn r kn 1 r

topological rigidity for hyperbolic manifolds soit m une variete de riemann complete ayant une courbure sectionnelle constante 1 et un volume fini soit m sa compactification variete de gromov margulis et on suppose que la dimension de m est 5 on montre qu une equivalence d homotopie h n n m m ou n est une variete compacte est homotopique a un homeomorphisme

an open collar theorem for 4 manifolds let m 4 be an open 4 manifold with boundary conditions are given under which m 4 is homeomorphic to m 0 1 applications include a 4 dimensional weak h cobordism theorem and a classification of weakly flat embeddings of 2 spheres in s 4 specific examples of n 2 spheres embedded in s n including n 4 are also discussed

reliability of perturbation theory in general relativity the relation between perturbation theory and exact solutions in general relativity is tackled by investigating the existence and properties of smooth one parameter families of solutions on the one hand the coefficients of the taylor expansion in the parameter of any given smooth family of solutions necessarily satisfy the hierarchy of perturbation equations on the other hand it is the converse question does any solution of the perturbation equations come from taylor expanding some family of exact solutions which is of importance for the mathematical justification of the use of perturbation theory this converse question is called the one of the reliability of perturbation theory using and completing recent results on the characteristic initial value problem the local reliability of perturbation theory for general relativity in vacuum is proven very generally this result is then generalized to the einstein yang mills equations and therefore in particular to the einstein maxwell ones

gap detection for similar and dissimilar gap markers detection thresholds for temporal gaps between markers of dissimilar frequency are usually elevated with respect to thresholds for gaps between markers of similar frequency because gaps between markers of dissimilar frequency represent both a spectrally based perceptual discontinuity as well as a temporal discontinuity it is not clear what factors underlie the threshold elevation this study sought to examine the effects of perceptual dissimilarities on gap detection the first experiment measured gap detection for configurations of narrow band gap markers comprised of pure tones frequency modulated tones and amplitude modulated tones the results showed that gap thresholds for frequency disparate pure tone markers were elevated with respect to isofrequency tonal markers but that perceptual discontinuities between markers restricted to the same frequency region did not uniformly elevate threshold the second experiment measured gap detection for configurations of markers where the leading and trailing markers could differ along the dimensions of bandwidth duration and pitch the results showed that in most cases gap detection deteriorated when the bandwidth of the two markers differed even when the spectral content of the narrower band marker was completely subsumed by the spectral content of the wider band marker this finding suggests that gap detection is sensitive to spectral dissimilarity between markers in addition to spectral discontinuity the effects of marker duration depended on the marker bandwidth pitch differences across spectrally similar markers had no effect