Normal all pseudo-Anosov subgroups of mapping class groups
نویسندگان
چکیده
منابع مشابه
Normal All Pseudo-anosov Subgroups of Mapping Class Groups
We construct the first known examples of nontrivial, normal, all pseudo-Anosov subgroups of mapping class groups of surfaces. Specifically, we construct such subgroups for the closed genus two surface and for the sphere with five or more punctures. Using the branched covering of the genus two surface over the sphere and results of Birman and Hilden, we show that if a projection of a reducible m...
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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 Σ be a closed orientable surface, and write Map(Σ) for its mapping class group — the group of self-homeomorphisms up to homotopy. The Nielsen-Thurston classification partitions the non-trivial elements of Map(Σ) into finite order, reducible, and pseudoanosov, the last being the “generic” case. A subgroup of Map(Σ) is purely pseudoanosov if every non-trivial element is pseudoanosov. Such a s...
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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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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: 2000
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2000.4.293