On the Chern character in Higher Twisted K-theory and spherical T-duality

TL;DR

This paper develops a Chern character for higher twisted K-theory derived from cohomotopy classes, establishing an isomorphism with higher twisted cohomology and computing spherical T-duality in broad contexts.

Contribution

It introduces a new Chern character for higher twists from cohomotopy, linking higher twisted K-theory and cohomology, and computes spherical T-duality in general cases.

Findings

Chern character induces an isomorphism between higher twisted K-theory and cohomology.

Established the framework for higher twists from cohomotopy classes.

Computed spherical T-duality in broad, general settings.

Abstract

In this paper, we construct for higher twists that arise from cohomotopy classes, the Chern character in higher twisted K-theory, that maps into higher twisted cohomology. We show that it gives rise to an isomorphism between higher twisted K-theory and higher twisted cohomology over the reals. Finally we compute spherical T-duality in higher twisted K-theory and higher twisted cohomology in very general cases.