منابع مشابه
Mod-two Cohomology of Symmetric Groups as a Hopf Ring
On the cohomology of BS• the second product · is cup product, which is zero for classes supported on disjoint components. The first product ⊙ is the relatively new transfer product first studied by Strickland and Turner [21], (see Definition 3.1). It is akin to the “induction product” in the representation theory of symmetric groups, which dates back to Young and has been in standard use [9, 22...
متن کاملDigital 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...
متن کاملSimplicial Cohomology with Coefficients in Symmetric Categorical Groups
In this paper we introduce and study a cohomology theory {Hn(−,A)} for simplicial sets with coefficients in symmetric categorical groups A. We associate to a symmetric categorical group A a sequence of simplicial sets {K(A, n)}n≥0, which allows us to give a representation theorem for our cohomology. Moreover, we prove that for any n ≥ 3, the functor K(−, n) is right adjoint to the functor ℘n, w...
متن کاملFirst non-abelian cohomology of topological groups II
In this paper we introduce a new definition of the first non-abelian cohomology of topological groups. We relate the cohomology of a normal subgroup $N$ of a topological group $G$ and the quotient $G/N$ to the cohomology of $G$. We get the inflation-restriction exact sequence. Also, we obtain a seven-term exact cohomology sequence up to dimension 2. We give an interpretation of the first non-a...
متن کاملCohomology of Groups
Notes on Kenneth Brown’s book Cohomology of Groups. 1. Some Homological Algebra 1.1. Review of Chain Complexes. Let R be a ring, and let (C, d) and (C ′, d′) be two chain complexes of left R-modules. Define a complex of abelian groups HR(C,C ′) as follows. Let HR(C,C )n = ∏ q∈Z HomR(Cq, C ′ q+n) and define the boundary map Dn by Dn(f) = d ′f − (−1)fd. 1.5. The Standard Resolution. For any group...
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: Journal of Algebra
سال: 2018
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2018.05.020