A topological index theorem for manifolds with corners

2005/07/29 by Bertrand Monthubert, Victor Nistor · 1 citation
Mathematics · #math.KT #math.OA #msc:22A22 #msc:47G30 #msc:58H05 #msc:58J22 #msc:58J40

paper · pdf · doi:10.1112/s0010437x11005458

published as Compositio Math. 148 (2012) 640-668 · 27 pages

arxiv created 2005/07/29 · arxiv updated 2019/02/20

Abstract

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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• Geometric obstructions to fully ellipticity for families of manifolds with corners