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‘Twice’ Equivariant C*-Index Theorem and the Index Theorem for Families

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Abstract

We prove the index theorem for elliptic operators acting on sections of bundles where the fiber is equal to a projective module over a C *-algebra in the situation of the action of a compact Lie group on this algebra as well as on the total space commuting with a symbol. For this purpose, we prove in particular the corresponding Thom isomorphism theorem. As an application, the equivariant family index theorem for a direct product of a base by the space of parameters is obtained.

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Authors
  1. Evgenij V. Troitsky
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Troitsky, E.V. ‘Twice’ Equivariant C*-Index Theorem and the Index Theorem for Families. Acta Applicandae Mathematicae 68, 39–70 (2001). https://doi.org/10.1023/A:1012217508793

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