On the first cohomology group of cofinite subgroups in surface mapping class groups
نویسندگان
چکیده
منابع مشابه
The Kazhdan Property of the Mapping Class Group of Closed Surfaces and the First Cohomology Group of Its Cofinite Subgroups
In the following we show that the mapping class group of a closed surface of genus 2 does not satisfy the Kazhdan property by constructing subgroups of nite index having a non-vanishing rst cohomology group. We also construct some subgroups of nite index in the mapping class group of a genus 3 surface and calculate their rst cohomology groups, which all turn out to be trivial. Most of the calcu...
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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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For Γ any group of finite virtual cohomological dimension and a prime p, we say that Γ is p-periodic, if there exists a positive integer k such that the Farrell cohomology groups Ĥ(Γ;M) and Ĥ(Γ;M) have naturally isomorphic p-primary components for all i ∈ Z and ZΓ-modules M . The p-period of Γ is defined as the least value of k (cf. [B]). For instance, if Γ is p-torsion free, then Γ is p-period...
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ژورنال
عنوان ژورنال: Topology
سال: 2001
ISSN: 0040-9383
DOI: 10.1016/s0040-9383(99)00066-x