Cut loci in lens manifolds

Sergei Anisov

doi:10.1016/j.crma.2006.01.025

Topology/Geometry

Cut loci in lens manifolds
[Cut loci dans les espaces lenticulaires]

Présenté par : Étienne Ghys

Sergei Anisov ¹

¹ Department of Mathematics, Utrecht University, P.O. Box 80.010, NL-3508 TA Utrecht, The Netherlands

Comptes Rendus. Mathématique, Volume 342 (2006) no. 8, pp. 595-600.

Résumé
Abstract

Les cut loci dans les variétés géométriques de dimension 3 par rapport à leurs métriques naturelles forment une classe remarquable d'épines. Par exemple, ces épines ont un petit nombre de sommets. En appliquant cette idée aux espaces lenticulaires, nous étudions des rapports entre leurs géométrie et topologie, les types combinatoires des enveloppes convexes des $Z_{p}$ -orbites, et des estimations de distance de rotation entre triangulations spécifiques d'un p-gone.

Cut loci in geometric three-manifolds equipped with their natural metrics are an interesting source of spines with small number of vertices. An application of this principle to lens manifolds reveals an interplay between their geometry and topology, combinatorial types of convex hulls of group orbits, and estimates of rotation distance between certain triangulations.

Reçu le : 2005-12-25
Accepté le : 2006-01-25
Publié le : 2006-03-09

DOI : 10.1016/j.crma.2006.01.025

Affiliations des auteurs :

Sergei Anisov ¹

¹ Department of Mathematics, Utrecht University, P.O. Box 80.010, NL-3508 TA Utrecht, The Netherlands

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     author = {Sergei Anisov},
     title = {Cut loci in lens manifolds},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {595--600},
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     year = {2006},
     doi = {10.1016/j.crma.2006.01.025},
     language = {en},
}

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Sergei Anisov. Cut loci in lens manifolds. Comptes Rendus. Mathématique, Volume 342 (2006) no. 8, pp. 595-600. doi : 10.1016/j.crma.2006.01.025. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.01.025/

Bibliographie
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