A topological index theorem for manifolds with corners

Details A topological index theorem for manifolds with corners A topological index theorem for manifolds with corners

2005-07-29

arxiv.org/abs/math/0507601v1

Mathematics

K-Theory and Homology

27 pages

Scientific paper

We define an analytic index and prove a topological index theorem for a non-compact manifold $M\_0$ with poly-cylindrical ends. We prove that an elliptic operator $P$ on $M\_0$ has an invertible perturbation $P+R$ by a lower order operator if an only if its analytic index vanishes. As an application, we determine the $K$-theory groups of groupoid $C^*$--algebras of manifolds with corners.

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