Atoroïdalité complète et annulation de l’invariant $\overline{\lambda }$ de Perelman

Suárez-Serrato, Pablo¹

¹ CIMAT CP : 36240, Guanajuato, Gto (México)

Séminaire de théorie spectrale et géométrie, Tome 26 (2007-2008), pp. 145-154.

Résumé

On résume les proprietés de l’invariant $\overline{\lambda }$ de Perelman, et en combinaison avec l’invariant de Yamabe on exprime certaines proprietés géométriques des variétés de dimension $3$ en fonction de $\overline{\lambda }$. On décrit des exemples d’annulation de $\overline{\lambda }$ en dimension $4$, où on trouve des liens entre l’effondrement et l’existence de métriques à courbure scalaire positive. On montre qu’une version d’atoroïdalité qu’on appelle atoroïdalité complète est détectée par $\overline{\lambda }$ sur les variétés de courbure négative ou nulle de dimension $\ge 3$.

Détail

DOI : 10.5802/tsg.265

Classification : 53C20, 53C23, 53C44
Mots-clés : effondrement, courbure scalaire, formes symplectiques, invariantes de Seiberg–Witten, courbure negative ou nulle, invariant de Yamabe invariant, invariant de Perelman

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