A basis of the Atiyah-Segal invariant polynomials

TL;DR

This paper characterizes the ring of invariant polynomials related to universal characteristic classes in twisted K-theory with infinite order twists, providing a basis and structure constants.

Contribution

It offers a detailed description of the ring of Atiyah-Segal invariant polynomials, including a basis and structure constants, for twisted K-theory with infinite order twists.

Findings

Established a basis for the ring of invariant polynomials.

Determined the structure constants of the ring.

Connected invariant polynomials with universal characteristic classes.

Abstract

For twisted K-theory whose twist is classified by a degree three integral cohomology of infinite order, universal even degree characteristic classes are in one to one correspondence with invariant polynomials of Atiyah and Segal. The present paper describes the ring of these invariant polynomials by a basis and structure constants.