Comptes Rendus
no. 7-8
Algebraic Geometry/Topology
Braids, conformal module and entropy
[Tresses, module conforme et entropie]

Présenté par : Etienne Ghys

Burglind Jöricke1
1 Centre de Recerca Matemàtica, Campus de Bellaterra, 08193 Bellaterra (Barcelona), Spain
Comptes Rendus. Mathématique, Volume 351 (2013) no. 7-8, pp. 289-293.

Le module conforme des classes de conjugaison de tresses est apparu dans un article de Lin et Gorin dans le cadre de leur intérêt pour le 13e problème de Hilbert. Cet invariant est la borne supérieure des modules conformes (dans le sens dʼAhlfors) de certains anneaux associés à la classe de conjugaison. Cette note affirme que le module conforme est inversement proportionnel à un invariant dynamique bien connu des tresses, lʼentropie. Lʼentropie est apparue dans le cadre de la théorie de Thurston des homéomorphismes de surfaces. Une application du concept de module conforme à la géométrie algébrique est donnée.

The conformal module of conjugacy classes of braids appeared in a paper of Lin and Gorin in connection with their interest in the 13th Hilbert Problem. This invariant is the supremum of conformal modules (in the sense of Ahlfors) of certain annuli related to the conjugacy class. This note states that the conformal module is inversely proportional to a popular dynamical braid invariant, the entropy. The entropy appeared in connection with Thurstonʼs theory of surface homeomorphisms. An application of the concept of conformal module to algebraic geometry is given.

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Accepté le :
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DOI : 10.1016/j.crma.2013.03.011
Burglind Jöricke 1

1 Centre de Recerca Matemàtica, Campus de Bellaterra, 08193 Bellaterra (Barcelona), Spain 
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Burglind Jöricke. Braids, conformal module and entropy. Comptes Rendus. Mathématique, Volume 351 (2013) no. 7-8, pp. 289-293. doi : 10.1016/j.crma.2013.03.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.03.011/

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