Groupoid C*-algebras and index theory on manifolds with singularities

Details Groupoid C*-algebras and index theory on manifolds with singularities Groupoid C*-algebras and index theory on manifolds with singularities

2001-05-10

arxiv.org/abs/math/0105085v1

Geom. Dedicata 100 (2003), 65-84

Mathematics

Differential Geometry

20 pages, latex and bibtex with 2 incorporated figures in postscript

Scientific paper

The simplest case of a manifold with singularities is a manifold M with boundary, together with an identification of the boundary with a product M1 x P, where P is a fixed manifold. The associated singular space is obtained by collapsing P to a point. When P = Z/k or S^1, we show how to attach to such a space a noncommutative C*-algebra that captures the extra structure. We then use this C*-algebra to give a new proof of the Freed-Melrose Z/k-index theorem and a proof of an index theorem for manifolds with S^1 singularities. Our proofs apply to the real as well as to the complex case. Applications are given to the study of metrics of positive scalar curvature.

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