A functional analysis proof of Gromov's polynomial growth theorem
[Une preuve de l'analyse fonctionnelle du théorème de la croissance polynomiale de Gromov]
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 51 (2018) no. 3, pp. 549-556.

Un résultat célèbre de Gromov affirme que tout groupe finiment engendré de croissance polynomiale contient un sous-groupe nilpotent d'indice fini. Des preuves alternatives de ce résultat ont été données par Kleiner, entre autres. Dans cette note, nous donnons une nouvelle preuve du théorème de Gromov, dans l'esprit de résultats de Shalom et Chifan-Sinclair, reposant sur l'analyse de la cohomologie réduite et la propriété H FD de Shalom.

The celebrated theorem of Gromov asserts that any finitely generated group with polynomial growth contains a nilpotent subgroup of finite index. Alternative proofs have been given by Kleiner and others. In this note, we give yet another proof of Gromov's theorem, along the lines of Shalom and Chifan-Sinclair, which is based on the analysis of reduced cohomology and Shalom's property H FD .

Publié le :
DOI : 10.24033/asens.2360
Classification : 20F65; 60B15, 43A07
Mots-clés : Reduced cohomology, hamonic 1-cocycles, cohomologie réduite, 1-cocycle harmonique 
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Ozawa, Narutaka. A functional analysis proof of Gromov's polynomial growth theorem. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 51 (2018) no. 3, pp. 549-556. doi : 10.24033/asens.2360. http://www.numdam.org/articles/10.24033/asens.2360/

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