twisted alexander polynomials detect fibered 3 manifolds a classical result in knot theory says that for a bered knot the alexander polynomial is monic and that the degree equals twice the genus of the knot this result has been generalized by various authors to twisted alexander polynomials and bered 3 manifolds in this paper we show that the conditions on twisted alexander polynomials are not only necessary but also sucient for a 3 manifold to be bered by previous work of the authors this result implies that if a manifold of the form s 1 n 3 admits a symplectic structure then n bers over s 1 in fact we will completely determine the symplectic cone of s 1 n in terms of the bered faces of the thurston norm ball of n

a new type of fixed point theorem in metric spaces abstract we prove a generalization of edelstein s fixed point theorem though there are thousands of fixed point theorems in metric spaces our theorem is a new type of theorem

fixed point theorems and convergence theorems for some generalized nonexpansive mappings we introduce some condition on mappings the condition is weaker than nonexpansiveness and stronger than quasinonexpansiveness we present fixed point theorems and convergence theorems for mappings satisfying the condition

symplectic mathbf s 1 times n 3 subgroup separability and vanishing thurston norm let be a closed oriented manifold a folklore conjecture states that admits a symplectic structure if and only if admits a fibration over the circle we will prove this conjecture in the case when is irreducible and its fundamental group satisfies appropriate subgroup separability conditions this statement includes manifolds with vanishing thurston norm graph manifolds and manifolds with surface subgroup separability a condition satisfied conjecturally by all hyperbolic manifolds our result covers in particular the case of 0 framed surgeries along knots of genus one the statement follows from the proof that twisted alexander polynomials decide fiberability for all the manifolds listed above as a corollary it follows that twisted alexander polynomials decide if a knot of genus one is fibered

knot adjacency and fibering it is known that the alexander polynomial detects fibered knots and 3 manifolds that fiber over the circle in this note we show that when the alexander polynomial becomes inconclusive the notion of knot adjacency can be used to obtain obstructions to the fibering of knots and of 3 manifolds as an application given a fibered knot k we construct infinitely many non fibered knots that share the same alexander module with k our construction also provides for every n n examples of irreducible 3 manifolds that cannot be distinguished by the cochran melvin finite type invariants of order n

generalized c conditions and related fixed point theorems in this manuscript the notion of c condition k suzuki fixed point theorems and convergence theorems for some generalized nonexpansive mappings j math anal appl 340 2008 1088 1095 is generalized some new fixed point theorems are obtained

a mollification approach for inverting the spherical mean radon transform the filtered backprojection algorithm is still one of the most important reconstruction methods in computed tomography it is based on explicit formulas for recovering mollified versions of the original unknown function in this paper we derive such formulas for the spherical mean radon transform with centers restricted to the boundary of a ball in two spatial dimensions we present an efficient implementation strategy that leads to a stable reconstruction algorithm of filtered backprojection type

fibred knots and twisted alexander invariants we study the twisted alexander invariants of fibred knots we establish necessary conditions on the twisted alexander invariants for a knot to be fibred and develop a practical method to compute the twisted alexander invariants from the homotopy type of a monodromy it is illustrated that the twisted alexander invariants carry more information on fibredness than the classical alexander invariants even for knots with trivial alexander polynomials

inversion of circular means and the wave equation on convex planar domains we study the problem of recovering the initial data of the two dimensional wave equation from values of its solution on the boundary w of a smooth convex bounded domain w r 2 as a main result we establish back projection type inversion formulas that recover any initial data with support in w modulo an explicitly computed smoothing integral operator k w for circular and elliptical domains the operator k w is shown to vanish identically and hence we establish exact inversion formulas of the back projection type in these cases similar results are obtained for recovering a function from its mean values over circles with centers on w both reconstruction problems are amongst others essential for the hybrid imaging modalities photoacoustic and thermoacoustic tomography

inversion of spherical means and the wave equation in even dimensions we establish inversion formulas of the so called filtered back projection type to recover a function supported in the ball in even dimensions from its spherical means over spheres centered on the boundary of the ball we also find several formulas to recover initial data of the form f 0 or 0 g for the free space wave equation in even dimensions from the trace of the solution on the boundary of the ball provided that the initial data has support in the ball

three dimensional manifolds kleinian groups and hyperbolic geometry 1 a conjectural picture of 3 manifolds a major thrust of mathematics in the late 19th century in which poincare had a large role was the uniformization theory for riemann surfaces that every conformai structure on a closed oriented surface is represented by a riemannian metric of constant curvature for the typical case of negative euler characteristic genus greater than 1 such a metric gives a hyperbolic structure any small neighborhood in the surface is isometric to a neighborhood in the hyperbolic plane and the surface itself is the quotient of the hyperbolic plane by a discrete group of motions the exceptional cases the sphere and the torus have spherical and euclidean structures three manifolds are greatly more complicated than surfaces and i think it is fair to say that until recently there was little reason to expect any analogous theory for manifolds of dimension 3 or more except perhaps for the fact that so many 3 manifolds are beautiful the situation has changed so that i feel fairly confident in proposing the

ricci curvature minimal volumes and seiberg witten theory we derive new sharp lower bounds for certain curvature functionals on the space of riemannian metrics of a smooth compact 4 manifold with non trivial seiberg witten invariants these allow one for example to exactly compute the infimum of the l 2 norm of ricci curvature for any complex surface of general type we are also able to show that the standard metric on any complex hyperbolic 4 manifold minimizes volume among all metrics satisfying a point wise lower bound on sectional curvature plus suitable multiples of the scalar curvature these estimates also imply new non existence results for einstein metrics

the exponentially convergent trapezoidal rule it is well known that the trapezoidal rule converges geometrically when applied to analytic functions on periodic intervals or the real line the mathematics and history of this phenomenon are reviewed and it is shown that far from being a curiosity it is linked with computational methods all across scientific computing including algorithms related to inverse laplace transforms special functions complex analysis rational approximation integral equations and the computation of functions and eigenvalues of matrices and operators

twisted alexander polynomials and symplectic structures let n be a closed oriented 3 manifold a folklore conjecture states that s 1 n admits a symplectic structure only if n admits a fibration over the circle the purpose of this paper is to provide evidence to this conjecture studying suitable twisted alexander polynomials of n and showing that their behavior is the same as of those of fibered 3 manifolds in particular we will obtain new obstructions to the existence of symplectic structures and to the existence of symplectic forms representing certain cohomology classes of s 1 n as an application of these results we will show that s 1 n p does not admit a symplectic structure where n p is the 0 surgery along the pretzel knot p 5 3 5 answering a question of peter kronheimer

two generalizations of some fixed point theorems the aim of this paper is to generalize two classical fixed point theorems given by bogin j bogin a generalization of a fixed point theorem of goebel kirk and shimi canad math bull 19 1976 7 12 and gregus m gregus a fixed point theorem in banach spaces boll un math ital a 5 17 1980 193 198 we also complement and extend some very recent results proved by suzuki t suzuki a generalized banach contraction principle that characterizes metric completeness proc amer math soc 136 2008 1861 1869

minimal genus in 4 manifolds with a free circle action abstract let n be a closed irreducible 3 manifold and assume n is not a graph manifold we improve for all but finitely many s 1 bundles m over n the adjunction inequality for the minimal complexity of embedded surfaces this allows us to completely determine the minimal complexity of embedded surfaces in all but finitely many s 1 bundles over a large class of 3 manifolds

twisted alexander norms give lower bounds on the thurston norm we introduce twisted alexander norms of a compact connected orientable 3 manifold with first betti number greater than one generalizing norms of mcmullen and turaev we show that twisted alexander norms give lower bounds on the thurston norm of a 3 manifold using these we completely determine the thurston norm of many 3 manifolds which are not determined by norms of mcmullen and turaev

effective discretization of direct reconstruction schemes for photoacoustic imaging in spherical geometries recently kernel methods for the recovery of a function from its spherical means in spherical acquisition geometry have been proposed we present efficient algorithms for these formulas in the two and three dimensional cases our scheme applies fourier techniques for certain convolution type integrals and discretizes physical space on a polar and a spherical grid respectively