Geodesic
Dimension and rank for mapping class groups
Jason A. Behrstock1 ; Yair N. Minsky2
1 Department of Mathematics, University of Utah, Salt Lake City, UT 84112, United States
2 Department of Mathematics, Yale University, New Haven, CT 06520, United States
Annals of mathematics, Tome 167 (2008) no. 3, pp. 1055-1077.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We study the large scale geometry of the mapping class group, $\mathcal{MCG}(S)$. Our main result is that for any asymptotic cone of $\mathcal{MCG}(S)$, the maximal dimension of locally compact subsets coincides with the maximal rank of free abelian subgroups of $\mathcal{MCG}(S)$. An application is a proof of Brock-Farb’s Rank Conjecture which asserts that $\mathcal{MCG}(S)$ has quasi-flats of dimension $N$ if and only if it has a rank $N$ free abelian subgroup. (Hamenstadt has also given a proof of this conjecture, using different methods.) We also compute the maximum dimension of quasi-flats in Teichmuller space with the Weil-Petersson metric.
DOI : 10.4007/annals.2008.167.1055

Jason A. Behrstock 1 ; Yair N. Minsky 2

1 Department of Mathematics, University of Utah, Salt Lake City, UT 84112, United States
2 Department of Mathematics, Yale University, New Haven, CT 06520, United States 
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Jason A. Behrstock; Yair N. Minsky. Dimension and rank for mapping class groups. Annals of mathematics, Tome 167 (2008) no. 3, pp. 1055-1077. doi : 10.4007/annals.2008.167.1055. http://geodesic.mathdoc.fr/articles/10.4007/annals.2008.167.1055/

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