Cohomology groups of the class groups over a Zpextension

Digital cohomology groups of certain minimal surfaces

In this study, we compute simplicial cohomology groups with different coefficients of a connected sum of certain minimal simple surfaces by using the universal coefficient theorem for cohomology groups. The method used in this paper is a different way to compute digital cohomology groups of minimal simple surfaces. We also prove some theorems related to degree properties of a map on digital sph...

Realization of a Certain Class of Semi-Groups as Value Semi-Groups of Valuations

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...

Cohomology 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.

On 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...