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arXiv · 1402.4996

Index theory for manifolds with Baas-Sullivan singularities

Robin J. Deeley
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Abstract

We study index theory for manifolds with Baas-Sullivan singularities using geometric K-homology with coefficients in a unital C*-algebra. In particular, we define a natural analog of the Baum-Connes assembly map for a torsion-free discrete group in the context of these singular spaces. The cases of singularities modelled on k-points (i.e., z/k-manifolds) and the circle are discussed in detail. In the case of the former, the associated index theorem is related to the Freed-Melrose index theorem; in the case of latter, the index theorem is related to work of Rosenberg.

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Robin J. Deeley. 2014-02-20. Index theory for manifolds with Baas-Sullivan singularities. https://arxiv.org/abs/1402.4996

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