Index theory and non-commutative geometry on foliated manifolds

TL;DR

This paper surveys the index theory for elliptic operators on foliated manifolds and explores related concepts in non-commutative geometry, highlighting recent advances and key results in the field.

Contribution

It provides a comprehensive overview of index theory and non-commutative geometry applications on foliated manifolds, summarizing recent developments.

Findings

Summarizes key results in tangentially elliptic operator index theory.

Highlights connections between foliated manifolds and non-commutative geometry.

Reviews advances in transversally elliptic operator analysis.

Abstract

This paper gives a survey of the index theory of tangentially elliptic and transversally elliptic operators on foliated manifolds as well as of related notions and results in non-commutative geometry.