The First Integral Cohomology of Pure Mapping Class Groups
نویسندگان
چکیده
منابع مشابه
The Center of Some Braid Groups and the Farrell Cohomology of Certain Pure Mapping Class Groups
In this paper we first show that many braid groups of low genus surfaces have their centers as direct factors. We then give a description of centralizers and normalizers of prime order elements in pure mapping class groups of surfaces with spherical quotients using automorphism groups of fundamental groups of the quotient surfaces. As an application, we use these to show that the p-primary part...
متن کاملFarrell cohomology of low genus pure mapping class groups with punctures
Abstract In this paper, we calculate the p-torsion of the Farrell cohomology for low genus pure mapping class groups with punctures, where p is an odd prime. Here, ‘low genus’ means g = 1, 2, 3; and ‘pure mapping class groups with punctures’ means the mapping class groups with any number of punctures, where the punctures are not allowed to be permuted. These calculations use our previous result...
متن کاملCohomology of mapping class groups and the abelian moduli space
We consider a surface Σ of genus g ≥ 3, either closed or with exactly one puncture. The mapping class group Γ of Σ acts symplectically on the abelian moduli space M = Hom(π1(Σ), U(1)) = Hom(H1(Σ), U(1)), and hence both L 2(M) and C(M) are modules over Γ. In this paper, we prove that both the cohomology groups H1(Γ, L2(M)) and H1(Γ,C∞(M)) vanish.
متن کاملOn the Farrell Cohomology of Mapping Class Groups
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...
متن کاملBounded Cohomology and Non-uniform Perfection of Mapping Class Groups
Using the existence of certain symplectic submanifolds in symplectic 4-manifolds, we prove an estimate from above for the number of singular fibers with separating vanishing cycles in minimal Lefschetz fibrations over surfaces of positive genus. This estimate is then used to deduce that mapping class groups are not uniformly perfect, and that the map from their second bounded cohomology to ordi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2020
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnaa229