Analysis of twisted supercharge families on product manifolds

Abstract

Twisted supercharge families on product manifolds TˆM have been applied in the analysis of the odd twisted K-theory. We shall suspend these families to the even twisted K-theory and solve their twisted families index problem. This is applied to give analytic representatives of the twisted K-theory classes on tori -including all the torsion classes.MSC: 19L50, 53C08, 19K56.