The Cohomology Of The Weak Stable Foliation Of Geodesic Flows

TL;DR

This paper computes the second cohomology of the weak stable foliation of geodesic flows, advancing understanding of the foliation's topological properties relevant to dynamical systems.

Contribution

It provides the first computation of the second dimension cohomology, completing the cohomological analysis of these foliations.

Findings

Computed the second dimension cohomology of the foliation.

Extended previous work on the first cohomology.

Contributed to the understanding of the foliation's topological structure.

Abstract

The leafwise cohomology of the weak stable foliation of the geodesic flows is very important in the study of the space of actions whose orbit foliation is the weak stable foliation of geodesic flows.The dimension one cohomology was computed by S.Matsumoto and Y.Mitsumatsu in [MM].In this article we compute the second dimension cohomology completing the study of the cohomology of these foliations.