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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)
In  we showed nonvaninishing of the universal index elements in the K-theory of the maximal C *-algebras of the fundamental groups of enlargeable spin manifolds. The underlying notion of enlargeability was the one from , involving contracting maps defined on finite covers of the given manifolds. In the paper at hand, we weaken this assumption to the… (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)
A well known conjecture in the theory of transformation groups states that if p is a prime and (Z/p) r acts freely on a product of k spheres, then r ≤ k. We prove this assertion if p is large compared to the dimension of the product of spheres. The argument builds on tame homotopy theory for non-simply connected spaces.
By results of Löffler and Comezaña, the Pontrjagin-Thom map from geometric G-equivariant bordism to homotopy theoretic equi-variant bordism is injective for compact abelian G. If G = S 1 ×.. .×S 1 , we prove that the associated fixed point square is a pull back square, thus confirming a recent conjecture of Sinha . This is used in order to determine the… (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=p-algebra H Ã ðX ; F p Þ, if H Ã 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)
We give explicit examples of degree 3 cohomology classes not Poincaré dual to submanifolds, and discuss the real-isability of homology classes by submanifolds with Spin c normal bundles.
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.