2021/05/10 by Michael Brandenbursky, Brandenbursky, Michael, Michał Marcinkowski +3 · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.DG #math.GR #math.GT #math.SG
paper · pdf · doi:10.48550/arxiv.2105.04658
17 pages. arXiv admin note: substantial text overlap with arXiv:1604.06953
arxiv created 2021/05/10 · openalex publication_date 2021/05/10 · arxiv updated 2021/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove a number of new results on the large-scale geometry of the Lp-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 Lp-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.