Homotopy invariance of relative eta-invariants and -algebra -theory

Author:
Navin Keswani

Journal:
Electron. Res. Announc. Amer. Math. Soc. **4** (1998), 18-26

MSC (1991):
Primary 19K56

DOI:
https://doi.org/10.1090/S1079-6762-98-00042-0

Published electronically:
April 1, 1998

MathSciNet review:
1613055

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Abstract: We prove a close cousin of a theorem of Weinberger about the homotopy invariance of certain relative eta-invariants by placing the problem in operator -theory. The main idea is to use a homotopy equivalence to construct a loop of invertible operators whose ``winding number" is related to eta-invariants. The Baum-Connes conjecture and a technique motivated by the Atiyah-Singer index theorem provides us with the invariance of this winding number under twistings by finite-dimensional unitary representations of .

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Additional Information

**Navin Keswani**

Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802

Email:
navin@math.psu.edu

DOI:
https://doi.org/10.1090/S1079-6762-98-00042-0

Keywords:
Eta-invariants,
$K$-theory

Received by editor(s):
January 28, 1998

Published electronically:
April 1, 1998

Additional Notes:
The author would like to thank Nigel Higson for his guidance with this project.

Communicated by:
Masamichi Takesaki

Article copyright:
© Copyright 1998
American Mathematical Society