Feuilleter
no. 5
Conformal Invariants of 3-Braids and Counting Functions
Burglind Jöricke1
1 IHES, 35 Route de Chartres, 91440 Bures-sur-Yvette, France
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 31 (2022) no. 5, pp. 1323-1341.

We consider a conformal invariant of braids, the extremal length with totally real horizontal boundary values Λtr. The invariant descends to an invariant of elements of ℬn∕𝒵n, the braid group modulo its center. We prove that the number of elements of ℬ3∕𝒵3 of positive Λtr grows exponentially. The estimate applies to obtain effective finiteness theorems in the spirit of the geometric Shafarevich conjecture over Riemann surfaces of second kind. As a corollary we obtain another proof of the exponential growth of the number of conjugacy classes of ℬ3∕𝒵3 with positive entropy not exceeding Y.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/afst.1721
Classification : 30F60, 30CXX, 37B40, 57MXX, 20F36
Mots-clés : Braids, extremal length, mapping classes, entropy, counting function

Burglind Jöricke 1

1 IHES, 35 Route de Chartres, 91440 Bures-sur-Yvette, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Burglind Jöricke. Conformal Invariants of 3-Braids and Counting Functions. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 31 (2022) no. 5, pp. 1323-1341. doi : 10.5802/afst.1721. https://afst.centre-mersenne.org/articles/10.5802/afst.1721/

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