#### 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
##### 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
Primary: 58B34