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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.

We consider a conformal invariant of braids, the extremal length with totally real horizontal boundary values Λ tr . The invariant descends to an invariant of elements of n 𝒵 n , the braid group modulo its center. We prove that the number of elements of 3 𝒵 3 of positive Λ tr 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 3 𝒵 3 with positive entropy not exceeding Y.

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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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     author = {Burglind J\"oricke},
     title = {Conformal {Invariants} of {3-Braids} and {Counting} {Functions}},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {1323--1341},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 31},
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     doi = {10.5802/afst.1721},
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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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