Hopf cyclic cohomology and Hodge theory for proper actions

Details Hopf cyclic cohomology and Hodge theory for proper actions Hopf cyclic cohomology and Hodge theory for proper actions

2010-02-23

arxiv.org/abs/1002.4404v2

Mathematics

Differential Geometry

17 pages

Scientific paper

We introduce a Hopf algebroid associated to a proper Lie group action on a smooth manifold. We prove that the cyclic cohomology of this Hopf algebroid is equal to the de Rham cohomology of invariant differential forms. When the action is cocompact, we develop a generalized Hodge theory for the de Rham cohomology of invariant differential forms. We prove that every cyclic cohomology class of the Hopf algebroid is represented by a generalized harmonic form. This implies that the space of cyclic cohomology of the Hopf algebroid is finite dimensional. As an application of the techniques developed in this paper, we discuss properties of the Euler characteristic for a proper cocompact action.

Affiliated with

Also associated with

No associations

Rating

Hopf cyclic cohomology and Hodge theory for proper actions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hopf cyclic cohomology and Hodge theory for proper actions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hopf cyclic cohomology and Hodge theory for proper actions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-259915