We prove the Conley conjecture for a closed symplectically aspherical symplectic manifold: a Hamiltonian diffeomorphism of a such a manifold has infinitely many periodic points. More precisely, we show that a Hamiltonian diffeomorphism with finitely many fixed points has simple periodic points of arbitrarily large period. This theorem generalizes, for instance, a recent result of Hingston estab...

Under mild assumptions on a group π, we prove that the class of complete Riemannian n–manifolds of uniformly bounded negative sectional curvatures and with the fundamental groups isomorphic to π breaks into finitely many tangential homotopy types. It follows that many aspherical manifolds do not admit complete negatively curved metrics with prescribed curvature bounds.

In this article we prove a special case of a conjecture of A. Abrams and R. Ghrist about fundamental groups of certain aspherical spaces. Specifically, we show that the n−point braid group of a linear tree is a right angled Artin group for each n.

a comprehensive study on the structural, electronic and nonlinear optical (nlo) properties of alumina nanostructures (al2o3)n with n = 2-5 belonging to the groups iii and vi dopants carried out by density functional theory. the nbo charges exhibit dopant atoms caused to the increasing charge transfer and introduces acceptor-donor model for nlo response of alumina nanostructures. under the influ...

We show that the product of infranilmanifolds with certain aspherical closed manifolds do not support Anosov diffeomorphisms. As a special case, we obtain that products of a nilmanifold and negatively curved manifolds of dimension at least 3 do not support Anosov diffeomorphisms. Mathematics Subject Classification. Primary 37D20; Secondary 55R10, 57R19, 37C25.

We prove an index theorem concerning the pushforward of flat B-vector bundles, where B is an appropriate algebra. We construct an associated analytic torsion form T . If Z is a smooth closed aspherical manifold, we show that T gives invariants of π∗(Diff(Z)).

Let X be a finite aspherical CW-complex whose fundamental group π1(X) possesses a subnormal series π1(X) ⊲ Gm ⊲ . . . ⊲ G0 with a non-trivial elementary amenable group G0. We investigate the L2-invariants of the universal covering of such a CW-complex X. We show that the NovikovShubin invariants αn(X̃) are positive. We further prove that the L2-torsion ρ(2)(X̃) vanishes if π1(X) has semi-integral...

We compute the Lagrangian Floer cohomology groups of certain tori in closed simply connected symplectic 4-manifolds arising from FintushelStern knot surgery. These manifolds are usually not symplectically aspherical. As a result of the computation we observe examples where HF (L0) = HF (L1) and L0 and L1 are smoothly isotopic but L0, L1 are not symplectically isotopic and are distinguished by H...

We give short new geometric proofs of theorems of Bogley and Pride and of Serre. Both follow quickly from a global fixed point theorem. The Bogley–Pride theorem concerns aspherical relative group presentations and was applied in [5] to the multivariable adjunction problem. Serre’s theorem is a basic result concerning group cohomology and finite subgroups.