### Abstract

We define an analytical index map and a topological index map for conical pseudomanifolds. These constructions generalize the analogous constructions used by Atiyah and Singer in the proof of their topological index theorem for a smooth, compact manifold M. A main new ingredient in our proof is a non-commutative algebra that plays in our setting the role of _{0}(T*M). We prove a Thom isomorphism between non-commutative algebras which gives a new example of wrong way functoriality in K-theory. We then give a new proof of the Atiyah-Singer Index Theorem using deformation groupoids and show how it generalizes to conical pseudomanifolds. We thus prove a topological index theorem for conical pseudomanifolds.

Original language | English (US) |
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Pages (from-to) | 1-35 |

Number of pages | 35 |

Journal | Journal fur die Reine und Angewandte Mathematik |

Issue number | 628 |

DOIs | |

State | Published - Mar 1 2009 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

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## Cite this

*Journal fur die Reine und Angewandte Mathematik*, (628), 1-35. https://doi.org/10.1515/CRELLE.2009.017