Groupoid C*algebras and index theory on manifolds with singularities
Abstract
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 FreedMelrose Z/kindex 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2001
 arXiv:
 arXiv:math/0105085
 Bibcode:
 2001math......5085R
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Operator Algebras;
 58J22 (Primary) 19K56;
 46L87;
 46L85;
 46L80 (Secondary)
 EPrint:
 20 pages, latex and bibtex with 2 incorporated figures in postscript