We consider a conformal invariant of braids, the extremal length with totally real horizontal boundary values . The invariant descends to an invariant of elements of , the braid group modulo its center. We prove that the number of elements of of positive 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 with positive entropy not exceeding .
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Mots-clés : Braids, extremal length, mapping classes, entropy, counting function
Burglind Jöricke 1
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@article{AFST_2022_6_31_5_1323_0,
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},
number = {5},
year = {2022},
doi = {10.5802/afst.1721},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1721/}
}
TY - JOUR AU - Burglind Jöricke TI - Conformal Invariants of 3-Braids and Counting Functions JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2022 SP - 1323 EP - 1341 VL - 31 IS - 5 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1721/ DO - 10.5802/afst.1721 LA - en ID - AFST_2022_6_31_5_1323_0 ER -
%0 Journal Article %A Burglind Jöricke %T Conformal Invariants of 3-Braids and Counting Functions %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2022 %P 1323-1341 %V 31 %N 5 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1721/ %R 10.5802/afst.1721 %G en %F AFST_2022_6_31_5_1323_0
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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