Finitely-Valued Cohomology Groups

Locally-finitely-valued Cohomology Groups

2000]Primary: 43A15; Secondary: 20F65, 20F18 GROUP COHOMOLOGY AND L-COHOMOLOGY OF FINITELY GENERATED GROUPS

In this paper G will always be a finitely generated, infinite group and S will always be a symmetric generating set for G. Let M be a right G-module. A 1cocycle with values in M is a map δ : G → M such that δ(gh) = (δ(h)) g + δ(g) for any g, h ∈ G; a 1-coboundary is a 1-cocycle of the form δ(g) = xg − x for some x ∈ M and for all g ∈ G. We denote by Z (G,M) the vector space of all 1-cocycles an...

Finitely Valued Indistinguishability Operators

Fuzzy equality relations or indistinguishability operators generalize the concepts of crisp equality and equivalence relations in fuzzy systems where inaccuracy and uncertainty is dealt with. They generate fuzzy granularity and are an essential tool in Computing with Words (CWW). Traditionally, the degree of similarity between two objects is a number between 0 and 1, but in many occasions this ...

Weakly Confluent Mappings and Finitely-generated Cohomology

In this paper we answer a question of Wayne Lewis by proving that if X is a one-dimensional, hereditarily indecomposable continuum and if HX(X) is finitely generated, then C(X), the hyperspace of subcontinua of X, has dimension 2. Let C(A) be the hyperspace of subcontinua of the continuum X with the topology determined by the Hausdorff metric. A classical theorem of J. L. Kelley [4] asserts tha...

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...