A topological index theorem for manifolds with corners

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 $C^{\ast }$--algebras of manifolds with corners.

27 pages

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Cited by in corpus (7)

• Geometric obstructions for Fredholm boundary conditions for manifolds with corners
• Atiyah-Bott index on stratified manifolds
• The Fredholm index for operators of tensor product type
• K-theory and index formulas for boundary groupoid C*-algebras
• On Fredholm boundary conditions on manifolds with corners I: Global corner's cycles obstructions
• Groupoids and singular manifolds
• Layer potentials C*-algebras of domains with conical points