Singular spaces, groupoids and metrics of positive scalar curvature

Abstract

We define and study, under suitable assumptions, the fundamental class, the index class and the rho class of a spin Dirac operator on the regular part of a spin stratified pseudomanifold. More singular structures, such as singular foliations, are also treated. We employ groupoid techniques in a crucial way; however, an effort has been made in order to make this article accessible to readers with only a minimal knowledge of groupoids. Finally, whenever appropriate, a comparison between classical microlocal methods and groupoids methods has been provided.

arXiv comment50 pages

References in corpus (7)

• Rho-classes, index theory and Stolz' positive scalar curvature sequence
• On the geometry of Riemannian manifolds with a Lie structure at infinity
• Groups with torsion, bordism and rho-invariants
• On the range of the relative higher index and the higher rho-invariant for positive scalar curvature
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Cited by in corpus (7)

• Positive scalar curvature on simply connected spin pseudomanifolds
• Positive Scalar Curvature on Spin Pseudomanifolds: the Fundamental Group and Secondary Invariants
• Slant products on the Higson-Roe exact sequence
• On analytic Todd classes of singular varieties
• Interior Kasparov product for $\varrho$-classes on Riemannian foliated bundles
• A topological approach to indices of geometric operators on manifolds with fibered boundaries
• The Fredholm index for operators of tensor product type