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 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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@article{CRMATH_2013__351_7-8_289_0, author = {J\"oricke, Burglind}, title = {Braids, conformal module and entropy}, journal = {Comptes Rendus. Math\'ematique}, pages = {289--293}, publisher = {Elsevier}, volume = {351}, number = {7-8}, year = {2013}, doi = {10.1016/j.crma.2013.03.011}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2013.03.011/} }
TY - JOUR AU - Jöricke, Burglind TI - Braids, conformal module and entropy JO - Comptes Rendus. Mathématique PY - 2013 SP - 289 EP - 293 VL - 351 IS - 7-8 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2013.03.011/ DO - 10.1016/j.crma.2013.03.011 LA - en ID - CRMATH_2013__351_7-8_289_0 ER -
Jöricke, Burglind. Braids, conformal module and entropy. Comptes Rendus. Mathématique, Tome 351 (2013) no. 7-8, pp. 289-293. doi : 10.1016/j.crma.2013.03.011. http://archive.numdam.org/articles/10.1016/j.crma.2013.03.011/
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