A Thom isomorphism in foliated de Rham theory

TL;DR

This paper establishes a Thom isomorphism theorem for differential forms within the context of foliated manifolds influenced by transverse Lie algebra actions, expanding the mathematical framework of foliated de Rham theory.

Contribution

It introduces a Thom isomorphism in foliated de Rham theory for transverse Lie algebra actions, a novel extension of classical results to foliated structures.

Findings

Thom isomorphism proven for foliated manifolds with transverse Lie algebra actions

Extension of classical de Rham theory to foliated vector bundles

Provides new tools for analyzing foliated geometric structures

Abstract

We prove a Thom isomorphism theorem for differential forms in the setting of transverse Lie algebra actions on foliated manifolds and foliated vector bundles.