Deformation of locally free actions and the leafwise cohomology

TL;DR

This paper explores how deformations of Lie group actions relate to leafwise cohomology in the context of foliation theory, providing insights into the structure of orbit foliations.

Contribution

It establishes a connection between the deformation theory of Lie group actions and leafwise cohomology of orbit foliations, advancing understanding in foliation deformation theory.

Findings

Link between deformation of Lie group actions and leafwise cohomology

Insights into orbit foliation structures

Foundational notes for further research in foliation deformations

Abstract

This is a note of the author's lectures at "Advanced courses in Foliation" in the research program "Foliation", which was held at the Centre de Recerca Mathematica in the May of 2010. In this note, we discuss about the relationship between deformation of actions of Lie groups and the leafwise cohomology of the orbit foliation.