The Atiyah-Patodi-Singer index theorem for Dirac operators over C*-algebras

Details The Atiyah-Patodi-Singer index theorem for Dirac operators over C*-algebras The Atiyah-Patodi-Singer index theorem for Dirac operators over C*-algebras

2009-01-04

arxiv.org/abs/0901.0381v1

Mathematics

Differential Geometry

56 pages

Scientific paper

We prove an Atiyah-Patodi-Singer index theorem for Dirac operators twisted by C*-vector bundles. We use it to derive a general product formula for Eta-forms and to define and study new Rho-invariants generalizing Lott's higher Rho-form. The higher Atiyah-Patodi-Singer index theorem of Leichtnam-Piazza can be recovered by applying the theorem to Dirac operators twisted by the Mishenko-Fomenko bundle associated to the reduced C*-algebra of the fundamental group.

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