Groupoids and an index theorem for conical pseudo-manifolds

Claire Debord, Jean Marie Lescure, Victor Nistor

Research output: Contribution to journalArticle

16 Scopus citations

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 languageEnglish (US)
Pages (from-to)1-35
Number of pages35
JournalJournal fur die Reine und Angewandte Mathematik
Issue number628
DOIs
StatePublished - Mar 1 2009

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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