Plongements quasiisom\'etriques du groupe de Heisenberg dans $L^p$, d'apr\`es Cheeger, Kleiner, Lee, Naor

TL;DR

This paper surveys Cheeger and Kleiner's theorem showing the Heisenberg group's nonembeddability into L^1, highlighting the limitations of embedding certain groups into Banach spaces.

Contribution

It provides an overview of the nonembeddability results for the Heisenberg group into L^1, emphasizing recent advances and techniques.

Findings

Heisenberg group cannot be embedded into L^1

Cheeger and Kleiner's nonembeddability theorem explained

Implications for metric geometry and Banach space theory

Abstract

This is a short survey of Cheeger and Kleiner's nonembeddability theorem for Heisenberg group into $L^1$.