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

@article{Brandenbursky2021TheSL, title={The Schwarz-Milnor lemma for braids and area-preserving diffeomorphisms}, author={Michael Brandenbursky and Michał Marcinkowski and Egor Shelukhin}, journal={Selecta Mathematica}, year={2021}, volume={28} }

We prove a number of new results on the large-scale geometry of the Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document}-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…

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