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We prove that in the Cayley graph of any braid group modulo its center Bn∕Z(Bn), equipped with Garside’s generating set, the axes of all pseudo-Anosov braids are strongly contracting. More generally, we consider a Garside group G of finite type with cyclic center. We prove that in the Cayley graph of G∕Z(G), equipped with the Garside generators, the axis of any Morse element is strongly contracting. As a consequence, we prove that Morse elements act loxodromically on the additional length graph of G.
Calvez, Matthieu 1 ; Wiest, Bert 2
@article{10_2140_agt_2024_24_4545,
author = {Calvez, Matthieu and Wiest, Bert},
title = {Morse elements in {Garside} groups are strongly contracting},
journal = {Algebraic and Geometric Topology},
pages = {4545--4574},
publisher = {mathdoc},
volume = {24},
number = {8},
year = {2024},
doi = {10.2140/agt.2024.24.4545},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.4545/}
}
TY - JOUR AU - Calvez, Matthieu AU - Wiest, Bert TI - Morse elements in Garside groups are strongly contracting JO - Algebraic and Geometric Topology PY - 2024 SP - 4545 EP - 4574 VL - 24 IS - 8 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.4545/ DO - 10.2140/agt.2024.24.4545 ID - 10_2140_agt_2024_24_4545 ER -
%0 Journal Article %A Calvez, Matthieu %A Wiest, Bert %T Morse elements in Garside groups are strongly contracting %J Algebraic and Geometric Topology %D 2024 %P 4545-4574 %V 24 %N 8 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.4545/ %R 10.2140/agt.2024.24.4545 %F 10_2140_agt_2024_24_4545
Calvez, Matthieu; Wiest, Bert. Morse elements in Garside groups are strongly contracting. Algebraic and Geometric Topology, Tome 24 (2024) no. 8, pp. 4545-4574. doi: 10.2140/agt.2024.24.4545
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