Related papers: Scalar Curvature And Transfer Maps In Spin And Spi…
Suppose $M$ is a closed $n$-dimensional spin$^c$ manifold with spin$^c$ structure $\sigma$ and associated spin$^c$ line bundle $L$. If one fixes a Riemannian metric $g$ on $M$ and a connection $\nabla_L$ on $L$, the generalized scalar…
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…
This thesis revolves around the Stolz' positive scalar curvature sequence: in particular adapted to the context of (G, F)-spaces, i.e. proper G-spaces with isotropy groups belonging to a family F of subgroups of G, and to that of manifolds…
In this paper, we study the space of metrics of positive scalar curvature using methods from coarse geometry. Given a closed spin manifold M with fundamental group G, Stephan Stolz introduced the positive scalar curvature exact sequence, in…
It is well-known that spin structures and Dirac operators play a crucial role in the study of positive scalar curvature metrics (psc-metrics) on compact manifolds. Here we consider a class of non-spin manifolds with "almost spin" structure,…
We study the effects of having multiple Spin structures on the partition function of the spacetime fields in M-theory. This leads to a potential anomaly which appears in the eta-invariants upon variation of the Spin structure. The main…
In this paper, we define a relative $L^2$-$\rho$-invariant for Dirac operators on odd-dimensional spin manifolds with boundary and show that they are invariants of the bordism classes of positive scalar curvature metrics which are collared…
Let $(M,L)$ be a (compact) non-spin spin$^c$ manifold. Fix a Riemannian metric $g$ on $M$ and a connection $A$ on $L$, and let $D_L$ be the associated spin$^c$ Dirac operator. Let $R^{tw}_{(g,A)}:=R_g + 2ic(\Omega)$ be the twisted scalar…
The Kreck-Stolz s invariant is used to distinguish connected components of the moduli space of positive scalar curvature metrics. We use a formula of Kreck and Stolz to calculate the s invariant for metrics on S^n bundles with nonnegative…
Let $N \subset M$ be a submanifold embedding of spin manifolds of some codimension $k \geq 1$. A classical result of Gromov and Lawson, refined by Hanke, Pape and Schick, states that $M$ does not admit a metric of positive scalar curvature…
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…
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…
We study the homotopy type of the space of metrics of positive scalar curvature on high-dimensional compact spin manifolds. Hitchin used the fact that there are no harmonic spinors on a manifold with positive scalar curvature to construct a…
The Kreck-Stolz $s$-invariant is a classic path-component invariant for the space and moduli space of positive scalar curvature metrics. It is an absolute (as opposed to relative) invariant, but this strength comes at the expense of being…
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…
Let $\big(M,g^{TM}\big)$ be a noncompact complete spin Riemannian manifold of even dimension $n$, with $k^{TM}$ denote the associated scalar curvature. Let $f\colon M\rightarrow S^{n}(1)$ be a smooth area decreasing map, which is locally…
In this paper we continue the study of positive scalar curvature (psc) metrics on a depth-1 Thom-Mather stratified space $M_\Sigma$ with singular stratum $\beta M$ (a closed manifold of positive codimension) and associated link equal to…
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 paper, we use localization algebras to study higher rho invariants of closed spin manifolds with positive scalar curvature metrics. The higher rho invariant is a secondary invariant and is closely related to positive scalar…
As shown by Gromov-Lawson and Stolz the only obstruction to the existence of positive scalar curvature metrics on closed simply connected manifolds in dimensions at least five appears on spin manifolds and is given by the non-vanishing of…