Vol. 304, No. 2, 2020

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

Xin Zhang

Vol. 304 (2020), No. 2, 753–766

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.

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Hopf algebroid, cyclic cohomology, boundaryless double, Hodge theory
Mathematical Subject Classification 2010
Primary: 58B34
Received: 22 May 2019
Revised: 13 August 2019
Accepted: 13 August 2019
Published: 12 February 2020
Xin Zhang
Wuhan University of Technology