We show that the mapping class group of a closed surface of higher genus admits a proper action on a nonpositively curved cube complex (which is however not simply connected). We use this information together with a construction of Ji and McPhearson to study its asymptotic geometry. As an application, we show that the covering dimension of the Gromov boundary of the curve graph is at most $4g − 6$ (which slightly improves a result of Gabai and is conjectured to be sharp).
De Yair Minsky
De Ursula Hamenstädt
De Dawid Kielak
De Radhika Gupta
De Anne Lonjou
De Piotr Przytycki
De Vincent Guirardel
De Federica Fanoni
De Corey Bregman
De Richard D. Wade
De Sebastian Hensel
De Stephen Coombes , Peter Liddle
De Ariane Trescases
De Albert Schwarz
De Stephen Coombes , Peter Liddle
De Victor Kleptsyn
De François-Xavier Vialard
