Geodesic
Homotopy invariance of relative eta-invariants and 𝐶*-algebra 𝐾-theory
Keswani, Navin1
1 Department of Mathematics, The Pennsylvania State University, University Park, PA 16802
Electronic research announcements of the American Mathematical Society, Tome 04 (1998), pp. 18-26.

Voir la notice de l'article provenant de la source American Mathematical Society

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 $K$-theory. The main idea is to use a homotopy equivalence $h:M \to M’$ 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 $\pi _{1}(M)$.
DOI : 10.1090/S1079-6762-98-00042-0

Keswani, Navin 1

1 Department of Mathematics, The Pennsylvania State University, University Park, PA 16802 
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Keswani, Navin. Homotopy invariance of relative eta-invariants and 𝐶*-algebra 𝐾-theory. Electronic research announcements of the American Mathematical Society, Tome 04 (1998), pp. 18-26. doi : 10.1090/S1079-6762-98-00042-0. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-98-00042-0/

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