The Joint Spectral Flow and Localization of the Indices of Elliptic   Operators
  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. 
Yosuke Kubota
math.KT