Convex cocompact subgroups of mapping class groups
نویسندگان
چکیده
منابع مشابه
Convex cocompact subgroups of mapping class groups
We develop a theory of convex cocompact subgroups of the mapping class group MCG of a closed, oriented surface S of genus at least 2, in terms of the action on Teichmüller space. Given a subgroup G of MCG de ning an extension 1 ! 1(S) ! ΓG ! G ! 1, we prove that if ΓG is a word hyperbolic group then G is a convex cocompact subgroup of MCG. When G is free and convex cocompact, called a Schottky ...
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Lattices and parabolic subgroups are the obvious examples of cocompact subgroups of a connected, semisimple Lie group with finite center. We use an argument of C. C. Moore to show that every cocompact subgroup is, roughly speaking, a combination of these. We study a cocompact subgroup H of a connected, semisimple Lie group G with finite center. The case where H is discrete is very important and...
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Mod(Σ) = Homeo(Σ)/Homeo0(Σ), where, Homeo(Σ) is the group of orientation preserving homeomorphisms of Σ and Homeo0(Σ) are those homeomorphisms isotopic to the identity. When Σ is a closed surface of genus g ≥ 1 then we denote Mod(Σ) by Γg. In this case it is well-known that Γg is isomorphic to a subgroup of index 2 in Out(π1(Σ)). When g = 1, the subgroup structure of Γ1 is well-understood since...
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Let g ≥ 3 and n ≥ 0, and let Mg,n be the mapping class group of a surface of genus g with n boundary components. We prove that Mg,n contains a unique subgroup of index 2g−1(2g − 1) up to conjugation, a unique subgroup of index 2g−1(2g + 1) up to conjugation, and the other proper subgroups ofMg,n are of index greater than 2g−1(2g+1). In particular, the minimum index for a proper subgroup of Mg,n...
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ژورنال
عنوان ژورنال: Geometry & Topology
سال: 2002
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2002.6.91