Index theory for manifolds with Baas–Sullivan singularities

  • Robin J. Deeley

    University of Colorado, Boulder, USA
Index theory for manifolds with Baas–Sullivan singularities cover
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Abstract

We study index theory for manifolds with Baas–Sullivan singularities using geometric -homology with coefficients in a unital -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 -points (i.e., $\mathbb Z/k\mathbb Z-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 the latter, the index theorem is related to work of Rosenberg.

Cite this article

Robin J. Deeley, Index theory for manifolds with Baas–Sullivan singularities. J. Noncommut. Geom. 12 (2018), no. 1, pp. 1–28

DOI 10.4171/JNCG/269