Bernhard Hanke

Learn More
Let M be a closed enlargeable spin manifold. We show non-triviality of the universal index obstruction in the K-theory of the maximal C *-algebra of the fundamental group of M. Our proof is independent from the injectivity of the Baum-Connes assembly map for π 1 (M) and relies on the construction of a certain infinite dimensional flat vector bundle out of a(More)
Using methods from coarse topology we show that fundamental classes of closed en-largeable manifolds map non-trivially both to the rational homology of their fundamental groups and to the K-theory of the corresponding reduced C *-algebras. Our proofs do not depend on the Baum– Connes conjecture and provide independent confirmation for specific predictions(More)
We show that for each discrete group Γ, the rational assembly map K * (BΓ) ⊗ Q → K * (C * max Γ) ⊗ Q is injective on classes dual to Λ * ⊂ H * (BΓ; Q), where Λ * is the sub-ring generated by cohomology classes of degree at most 2 (and where the pairing uses the Chern character). Our result implies homotopy invari-ance of higher signatures associated to(More)
Let Z=p act on an F p-Poincaré duality space X, where p is an odd prime number. We derive a formula that expresses the F p-Witt class of the fixed point set X Z=p in terms of the F p ½Z=pŠ-algebra H à ðX ; F p Þ, if H à ðX ; Z ð pÞ Þ does not contain Z=p as a direct summand. This extends previous work of Alexander and Hamrick, where the orientation class of(More)
We describe an explicit chain map from the standard resolution to the minimal resolution for the finite cyclic group Z k of order k. We then demonstrate how such a chain map induces a " Z k-combinatorial Stokes theorem " , which in turn implies " Dold's theorem " that there is no equivariant map from an n-connected to an n-dimensional free Z k-complex. Thus(More)
  • B Hanke, D Kotschick, J Wehrheim
  • 2008
We prove that many simply connected symplectic four-manifolds dissolve after connected sum with only one copy of S 2 × S 2. For any finite group G that acts freely on the three-sphere we construct closed smooth four-manifolds with fundamental group G which do not admit metrics of positive scalar curvature, but whose universal covers do admit such metrics.