Hopf cyclic cohomology for noncompact $G$-manifolds with boundary

Xin Zhang

Vol. 304 (2020), No. 2, 753–766

DOI: 10.2140/pjm.2020.304.753

Abstract

We introduce a differential graded Hopf algebroid associated to a proper Lie group action on an oriented manifold with boundary and prove that the cyclic cohomology of this Hopf algebroid is equal to the relative de Rham cohomology of invariant differential forms. When the action is cocompact, by investigating the boundaryless double of an oriented manifold with boundary, we prove that the cyclic cohomology of the above Hopf algebroid is of finite dimension.

Keywords

Hopf algebroid, cyclic cohomology, boundaryless double, Hodge theory

Mathematical Subject Classification 2010

Primary: 58B34

Milestones

Received: 22 May 2019

Revised: 13 August 2019

Accepted: 13 August 2019

Published: 12 February 2020