Géométrie systolique et technique de régularisation
Séminaire de théorie spectrale et géométrie, Volume 31 (2012-2014), pp. 1-41.

L’objectif de ce texte est de présenter la notion de systole d’une variété riemannienne et de faire un survol de la géométrie systolique. On illustrera aussi une technique fondamentale, appelée technique de régularisation, qui est à la base de plusieurs résultats essentiels de géométrie systolique. Je détaillerai comment cette technique permet d’estimer les nombres de Betti d’une variété asphérique (d’après Gromov), et comment elle permet de relier l’entropie volumique à la systole et au volume systolique d’une variété riemannienne (d’après Sabourau).

DOI: 10.5802/tsg.292
Keywords: Cycles géométriques, systole, volume systolique, espace d’Eilenberg-McLane, variété asphérique, nombres de Betti
Bulteau, Guillaume 1

1 Institut de Mathématiques et de Modélisation de Montpellier (I3M) UMR 5149 CNRS - Université Montpellier 2 Case courrier 051 34095 Montpellier cedex 5 (France)
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Bulteau, Guillaume. Géométrie systolique et technique de régularisation. Séminaire de théorie spectrale et géométrie, Volume 31 (2012-2014), pp. 1-41. doi : 10.5802/tsg.292. http://www.numdam.org/articles/10.5802/tsg.292/

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