A note on the equivariant Chern character in Noncommutative Geometry

2023/04/07 by Bjarne Kosmeijer, Hessel Posthuma, Kosmeijer, Bjarne +1
Mathematics · #19D55 #46L87 #55N91 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2304.03680

openalex publication_date 2023/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a smooth action of a Lie group on a manifold, we give two constructions of the Chern character of an equivariant vector bundle in the cyclic cohomology of the crossed product algebra. The first construction associates a cycle to the vector bundle whose structure maps are closely related to Getzler's model for equivariant cohomology. The second construction uses a direct map between this model and the (periodic) cyclic cohomology localized at the unit element. Finally, it is shown that the two constructions are equivalent when the action is proper.

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