universal amplitude ratios for self avoiding walks on the kagome lattice we have calculated exactly the number the mean square end to end distance the mean square radius of gyration and the mean square distance of a monomer from the origin for n step self avoiding walks on the kagome lattice up to 30 steps we have estimated the connective constant and the critical amplitudes our numerical results are consistent with the theoretical prediction by cardy and saleur 1989 on the universality for certain amplitude ratios

universal amplitude combinations for self avoiding walks and polygons on the honeycomb lattice abstract we have calculated exactly the mean square end to end distance the mean square radius of gyration and the mean square distance of a monomer from the origin for n step self avoiding walks on the honeycomb lattice up to 46 steps we also calculated the mean square radius of gyration and moments of area for n step self avoiding polygons on the honeycomb lattice up to 60 steps we estimated the critical amplitudes and our numerical results are consistent with the theoretical predictions by the universality for certain amplitude combinations

some product formulae for nonsimply connected surgery problems for an n dimensional normal map f m n with finite fundamental group 7 n x and pl 1 torsion kernel z g modules k m the surgery obstruction a f e lh z g is expressed in terms of the projective classes k m e k0 z 7 assuming k m 0 if n 2i this expression is used to evaluate in certain cases the surgery obstruction o g e lh z g1 x of the m n dimensional normal map g 1 x f m1 x m m1 x n defined by product with an m dimensional manifold m where gl 1 ml1 a key problem in surgery theory is to understand how to calculate the surgery obstructions for surgery problems f mn nn where f is a degree 1 normal map and mn nn are closed n dimensional manifolds c t c wall 20 has pointed out that the problem determines an element a f e on b l n x g top b l n x pt and there is a map e q abl n x g top b 7r n x pt l t n so that the surgery obstruction a f is e a f wall also pointed out that if vl n is finite then a f is already determined by restriction to the 2 sylow subgroup of 7t1 and the groups l t have been extensively studied when v is a finite 2 group see e g pardon 12 carlssonmilgram 3 5 hambleton milgram 9 wall 21 and bak kolster 1 indeed the projective l groups l 7t are completely known and the groups l h 7 and l 7r are effectively computable in tems of certain additional facts about ko z v and wh st so further progress depends on studying the map e for the projective l groups lp t with 7t a finite 2 group this was done by l taylor b williams 18 and independently by i hambleton 8 but for the more basic case of lh 7t our information is much more limited there are some key examples cappell shaneson 2 taylor williams 18 which show that this problem is much harder but general information is hard to come by received by the editors june 3 1985 1980 mathematics subject classification 1985 revision primary 57r67 1986 american mathematical society 0002 9947 86 1 00 25 per page

homotopy self equivalences of 4 manifolds we establish a braid of interlocking exact sequences containing the group of homotopy self equivalences of a smooth or topological 4 manifold the braid is computed for manifolds whose fundamental group is finite of odd order

universal distance ratios for 2d saws series results the mean square distance of a monomer to the origin and the mean square distance of the centre of mass to the origin are studied by exact enumeration on the square and triangular lattices the numerical results are inconsistent with the theoretical prediction of cardy and saleur 1989 by more than fifteen times the numerical uncertainty in the authors calculation

universal amplitude ratios for three dimensional self avoiding walks we have calculated exactly the number the mean square end to end distance the mean square radius of gyration and the mean square distance of a monomer from the origin for n step self avoiding walks on the simple cubic diamond body centred cubic and face centred cubic lattices respectively up to 20 30 16 and 13 steps by a computer two universal amplitude ratios are estimated

characteristic fixed point sets of semifree actions on spheres a group action is semifree if it is free away from its fixed point set p a smith showed that when a finite group of orderqacts semifreely on a sphere the fixed set is a modqhomology sphere conversely given a modqhomology sphere as a subset of a sphere one may try to construct a group action on the sphere fixing the subset the converse question was first systematically studied by jones and then by many others in this note we give new numerical congruences satisfied by the homology of the fixed sets and give a definitive solution to the problem for characteristic fixed point sets c 1999 john wiley sons inc

universal amplitude combinations for self avoiding walks polygons and trails the authors give exact relations for a number of amplitude combinations that occur in the study of self avoiding walks polygons and lattice trails in particular they elucidate the lattice dependent factors which occur in those combinations which are otherwise universal show how these are modified for oriented lattices and give new results for amplitude ratios involving even moments of the area of polygons they also survey numerical results for a wide range of amplitudes on a number of oriented and regular lattices and provide some new ones

comment on the universality class of self avoiding walks on a two layer square lattice abstract we have calculated exactly the mean square radius of gyration and the mean square distance of a monomer from the origin for n step self avoiding walks on a two layer square lattice up to 24 steps we estimated two universal amplitude ratios and the results provide additional evidence that self avoiding walks on a two layer lattice belongs to the same universality class as the self avoiding walk on a planar lattice

universal amplitude combinations for self avoiding walks and polygons on directed lattices two directed lattices the l lattice and manhattan lattice are studied we have calculated exactly the number the mean square end to end distance the mean square radius of gyration and the mean square distance of a monomer from the origin for n step self avoiding walks on the l lattice and manhattan lattice for up to 60 and 50 steps respectively we have also computed the number and mean square radius of gyration for self avoiding polygons on the l lattice and manhattan lattice for up to 80 and 60 steps respectively we have estimated the critical amplitudes and our numerical results are consistent with the conjecture of universality for certain amplitude combinations however some amplitude combinations have values different from the corresponding values for undirected lattices

integral cohomology and detection of w basic 2 groups we compute the cohomology h g z w of all w basic 2 groups g w with integral coefficients twisted by the orientation character w we also calculate appropriate restiction maps and thus prove that the cohomology of any w basic group is detected by subgroups isomorphic to one of five types and we provide a sample application of this main theorem

enumeration of self avoiding walks on the square lattice we describe a new algorithm for the enumeration of self avoiding walks on the square lattice using up to 128 processors on a hp alpha server cluster we have enumerated the number of self avoiding walks on the square lattice to length 71 series for the metric properties of mean square end to end distance mean square radius of gyration and mean square distance of monomers from the end points have been derived to length 59 an analysis of the resulting series yields accurate estimates of the critical exponents and confirming predictions of their exact values likewise we obtain accurate amplitude estimates yielding precise values for certain universal amplitude combinations finally we report on an analysis giving compelling evidence that the leading non analytic correction to scaling exponent 1 3 2

self avoiding walks neighbour avoiding walks and trails on semiregular lattices we study self avoiding and neighbour avoiding walks and lattice trails on two semiregular lattices the lattice and the lattice for the lattice we find the exact connective constant for both self avoiding walks neighbour avoiding walks and trails for the lattice we generate long series which permit the accurate estimation of the connective constant for self avoiding walks and trails

semicharacteristics bordism and free group actions in this paper we give characteristic class formulae for all semicharac teristic classes of all compact closed manifolds with finite fundamental groups these invariants are identified with elements in certain odd l groups and ex actly which elements occur is specified an appendix calculates the cohomology of the model groups needed a second appendix determines the structure of the l groups needed the euler characteristic of an odd dimensional manifold is zero a natural substitute is a semicharacteristic an alternating sum of the homology up to the middle dimension study of semicharacteristics was initiated by kervaire k who examined their role in differential topology and geometry the first semicharacteristic bordism invariant was introduced by derham it turns out k xx 2 m2k x k l diffl ff f a j i i

universal distance ratios for two dimensional polymers by using a quantitative version of the c theorem in conformal theories the authors determine some universal geometrical features of two dimensional critical systems with emphasis on the ratios of mean square distances for polymers

universal distance ratios for 2d saws monte carlo and exact series results the mean square distance of a monomer to the origin and the mean square distance of the centre of mass to the origin are studied by monte carlo and exact series methods on the square and lattice the numerical results give strong evidence of a discrepancy with the theoretical prediction of cardy and saleur 1989 based on conformal invariance theory

universal amplitude combinations for self avoiding polygons on the kagome lattice abstract we have calculated exactly the number the mean square radius of gyration and moments of area for n step self avoiding polygons on the kagome lattice up to 36 steps we estimated the critical amplitudes and our numerical results are consistent with the theoretical predictions by the universality for certain amplitude combinations

upper and lower bounds for the connective constants of self avoiding walks on the archimedean and laves lattices we give improved upper and lower bounds for the connective constants of self avoiding walks on a class of lattices including the archimedean and laves lattices the lower bounds are obtained by using kesten s method of irreducible bridges with an appropriate generalization for weakly regular lattices the upper bounds are obtained as the largest eigenvalue of a certain transfer matrix the obtained bounds show that in the studied class of lattices the connective constant is increasing in the average degree of the lattice we also discuss an alternative measure of average degree

surgery with finite fundamental group the relationship between the topology of manifolds and homotopy theory has been analysed by surgery 1 18 28 31 however the effectiveness of this analysis depends on being able to compute surgery obstructions in this paper we introduce a new technique for evaluating the weakly simple surgery obstructions for degree 1 normal maps of closed manifolds and apply it to oriented manifolds with finite fundamental group our main result is theorem a below let x dx be a finite poincare pair of dimension n and a top bundle over x which is stably fibre homotopy equivalent to the spivak normal fibre space v let m dm be a compact n dimensional manifold and let

topological equivalence of linear representations for cyclic groups i in the two parts of this paper we prove that the reidemeister torsion invariants determine topological equivalence of g representations for g a finite cyclic group

uniqueness of boundary blowup solutions to k curvature equation abstract we consider the boundary blowup problem for the k curvature equation i e h k u f u g d u in an n dimensional domain with the boundary condition u x as dist x 0 we prove the uniqueness result under some hypotheses