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This article is available for purchase or by subscription. See below.
Abstract
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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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Keywords
Hopf algebroid, cyclic cohomology, boundaryless double,
Hodge theory
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Mathematical Subject Classification 2010
Primary: 58B34
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Milestones
Received: 22 May 2019
Revised: 13 August 2019
Accepted: 13 August 2019
Published: 12 February 2020
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