On the dimension of CAT(0) spaces where mapping class groups act
نویسندگان
چکیده
منابع مشابه
On the Dimension of Cat(0) Spaces Where Mapping Class Groups Act
Whenever the mapping class group of a closed orientable surface of genus g acts by semisimple isometries on a complete CAT(0) space of dimension less than g it fixes a point.
متن کاملDimension and Rank for Mapping Class Groups
We study the large scale geometry of the mapping class group, MCG. Our main result is that for any asymptotic cone of MCG, the maximal dimension of locally compact subsets coincides with the maximal rank of free abelian subgroups of MCG. An application is a proof of Brock-Farb’s Rank Conjecture which asserts that MCG has quasi-flats of dimension N if and only if it has a rank N free abelian sub...
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The mapping class group of a topological space is the group of self-homeomorphisms modulo the equivalence relation of isotopy. For 2-manifolds (of finite type), it is a discrete group which is known (see [M, HI, H2, H3, H4]) to share many of the properties of arithmetic subgroups of linear algebraic groups, although it is not arithmetic. In this note we describe the results of [Ml], which show ...
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چکیده ندارد.
15 صفحه اولMapping Class Groups and Moduli Spaces of Curves
It is classical that there is a very strong relation between the topology of Mg, the moduli space of smooth projective curves of genus g, and the structure of the mapping class group Γg, the group of homotopy classes of orientation preserving diffeomorphisms of a compact orientable surface of genus g. The geometry of Mg, the topology of Mg, and the structure of Γg are all intimately related. Un...
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ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2012
ISSN: 1435-5345,0075-4102
DOI: 10.1515/crelle.2011.172