# Index theory for manifolds with Baas–Sullivan singularities

### Robin J. Deeley

University of Colorado, Boulder, USA

## 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., $\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