Related papers: An appendix to a paper by B. Hanke and T. Schick

We prove the vanishing of higher A-hat-genera, in the sense of Browder and Hsiang, on smooth manifolds with effective circle actions and with finite second and fourth homotopy groups

Positiveness of scalar curvature and Ricci curvature requires vanishing the obstruction $\theta(M)$ which is computed in some KK-theory of C*-algebras index as a pairing of spin Dirac operator and Mishchenko bundle associated to the…

In a recent paper, the authors proved that no spin foliation on a compact enlargeable manifold with Hausdorff homotopy graph admits a metric of positive scalar curvature on its leaves. This result extends groundbreaking results of…

We prove several results about the vanishing of the elliptic genus on positively curved Spin manifolds with logarithmic symmetry rank. The proofs are based on the rigidity of the elliptic genus and Kennard's improvement of the Connectedness…

We extend the vanishing theorem for the Seiberg-Witten invariants of a manifold with positive scalar curvature to the case when the curvature is allowed to be negative on a set of small volume. (The precise curvature bounds are described in…

We show in this short note that if a rational linear combination of Pontrjagin numbers vanishes on all simply-connected $4k$-dimensional closed connected and oriented spin manifolds admitting a Riemannian metric whose Ricci curvature is…

The Gromov-Lawson-Rosenberg-conjecture for a group G states that a closed spin manifold M^n (n>4) with fundamental group G admits a metric with positive scalar curvature if and only if its C^*-index A(M) in KO_n(C^*_r(G)) vanishes. We prove…

Gromov and Lawson conjectured that a closed spin manifold M of dimension n with fundamental group pi admits a metric with positive scalar curvature if and only if an associated element in KO_n(B pi) vanishes. In this note we present counter…

This is a continuation of our previous work with Botvinnik on the nontriviality of the secondary index invariant on spaces of metrics of positive scalar curvature, in which we take the fundamental group of the manifolds into account. We…

We generalize classical theorems due to Lichnerowicz and Hitchin on the existence of Riemannian metrics of positive scalar curvature on spin manifolds to the case of foliated spin manifolds. As a consequence, we show that there is no…

Let $M$ be a closed aspherical manifold. Assume that the rational strong Novikov conjecture holds for $\pi_1(M)$. We show that on any spin surgery of $M$ along a region whose induced homomorphism on the fundamental group is trivial, every…

We give the first examples of rationally inessential but macroscopically large manifolds. Our manifolds are counterexamples to the Dranishnikov rationality conjecture. For some of them we prove that they do not admit a metric of positive…

In this paper we develop methods to extend the minimal hypersurface approach to positive scalar curvature problems to all dimensions. This includes a proof of the positive mass theorem in all dimensions without a spin assumption. It also…

We construct geometric generators of the effective $S^1$-equivariant Spin- (and oriented) bordism groups with two inverted. We apply this construction to the question of which $S^1$-manifolds admit invariant metrics of positive scalar…

We discuss a conjecture of Gromov and Lawson, later modified by Rosenberg, concerning the existence of metrics of positive scalar curvature. It says that a closed spin manifold $M$ of dimension $n\ge 5$ has such a metric if and only if the…

In this article we study the space of positive scalar curvature metrics on totally nonspin manifolds with spin boundary. We prove that for such manifolds of certain dimensions, those spaces are not connected and have nontrivial fundamental…

In this short note we show how the higher index theory can be used to prove results concerning the non-existence of complete riemannian metric with uniformly positive scalar curvature at infinity. By improving some classical results due to…

For a finitely generated discrete group $\Gamma$ acting properly on a spin manifold $M$, we formulate new topological obstructions to $\Gamma$-invariant metrics of positive scalar curvature on $M$ that take into account the cohomology of…

We extend the deep and important results of Lichnerowicz, Connes, and Gromov-Lawson which relate geometry and characteristic numbers to the existence and non-existence of metrics of positive scalar curvature (PSC). In particular, we show:…

We prove a Riemannian positive mass theorem for asymptotically flat spin manifolds with hypersurface singularities. Unlike earlier results, some components of the singular set may be mean-concave, provided that other components of the…