On the nonexistence of higher twistings

TL;DR

This paper proves that higher twistings do not exist for the Borel cohomology theory related to G-equivariant K-theory over a point, simplifying the classification of twistings to specific cohomology groups.

Contribution

It establishes the nonexistence of higher twistings for a key cohomology theory, clarifying the structure of twistings over a point for compact Lie groups.

Findings

Higher twistings are absent for the specified cohomology theory.

Twistings over a point are classified by H^{1}(BG,Z/2) × H^{3}(BG,Z).

Simplifies the understanding of twistings in equivariant K-theory.

Abstract

In this note we show that there are no higher twistings for the Borel cohomology theory associated to G-equivariant K-theory over a point and for a compact Lie group G. Therefore, twistings over a point for this theory are classified by the group H^{1}(BG,Z/2)\x H^{3}(BG,Z)