Vol. 1, No. 1, 2016

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The joint spectral flow and localization of the indices of elliptic operators

Yosuke Kubota

Vol. 1 (2016), No. 1, 43–83
DOI: 10.2140/akt.2016.1.43
Abstract

We introduce the notion of the joint spectral flow, which is a generalization of the spectral flow, by using Segal’s model of the connective K-theory spectrum. We apply it for some localization results of indices motivated by Witten’s deformation of Dirac operators, and rephrase some analytic techniques in terms of topology.

Keywords
index theory, spectral flow, localization, connective $K$-theory, $KK$-theory
Mathematical Subject Classification 2010
Primary: 19K56
Secondary: 19K35, 19L41
Milestones
Received: 25 December 2014
Accepted: 30 December 2014
Published: 31 July 2015
Authors
Yosuke Kubota
Graduate School of Mathematical Sciences
The University of Tokyo
3-8-1 Komaba
Meguro-ku 153-8914
Japan