The Schwarz-Milnor lemma for braids and area-preserving diffeomorphisms

Autor:	Brandenbursky, Michael, Marcinkowski, Michał, Shelukhin, Egor
Rok vydání:	2021
Předmět:	Mathematics - Geometric Topology Mathematics - Differential Geometry Mathematics - Group Theory Mathematics - Symplectic Geometry
Druh dokumentu:	Working Paper
Popis:	We prove a number of new results on the large-scale geometry of the $L^p$-metrics on the group of area-preserving diffeomorphisms of each orientable surface. Our proofs use in a key way the Fulton-MacPherson type compactification of the configuration space of $n$ points on the surface due to Axelrod-Singer and Kontsevich. This allows us to apply the Schwarz-Milnor lemma to configuration spaces, a natural approach which we carry out successfully for the first time. As sample results, we prove that all right-angled Artin groups admit quasi-isometric embeddings into the group of area-preserving diffeomorphisms endowed with the $L^p$-metric, and that all Gambaudo-Ghys quasi-morphisms on this metric group coming from the braid group on $n$ strands are Lipschitz. This was conjectured to hold, yet proven only for low values of $n$ and the genus $g$ of the surface. Comment: 17 pages. arXiv admin note: substantial text overlap with arXiv:1604.06953
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2105.04658 Zobrazit plný text záznamu View this record from Arxiv