direct homology group

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• Group cohomology — This article is about homology and cohomology of a group. For homology or cohomology groups of a space or other object, see Homology (mathematics). In abstract algebra, homological algebra, algebraic topology and algebraic number theory, as well… …   Wikipedia

• Group (mathematics) — This article covers basic notions. For advanced topics, see Group theory. The possible manipulations of this Rubik s Cube form a group. In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines …   Wikipedia

• Symmetric group — Not to be confused with Symmetry group. A Cayley graph of the symmetric group S4 …   Wikipedia

• Coxeter group — In mathematics, a Coxeter group, named after H.S.M. Coxeter, is an abstract group that admits a formal description in terms of mirror symmetries. Indeed, the finite Coxeter groups are precisely the finite Euclidean reflection groups; the symmetry …   Wikipedia

• Simplicial homology — In mathematics, in the area of algebraic topology, simplicial homology is a theory with a finitary definition, and is probably the most tangible variant of homology theory. Simplicial homology concerns topological spaces whose building blocks are …   Wikipedia

• Compactly-supported homology — In mathematics, a homology theory in algebraic topology is compactly supported if, in every degree n, the relative homology group Hn(X, A) of every pair of spaces (X, A) is naturally isomorphic to the direct limit of the nth relative homology… …   Wikipedia

• Steinberg group (K-theory) — In algebraic K theory, a field of mathematics, the Steinberg group operatorname{St}(A) of a ring A , is the universal central extension of the commutator subgroup of the stable general linear group.It is named after Robert Steinberg, and is… …   Wikipedia

• Mapping class group — In mathematics, in the sub field of geometric topology, the mapping class group is an important algebraic invariant of a topological space. Briefly, the mapping class group is a discrete group of symmetries of the space. Contents 1 Motivation 2… …   Wikipedia

• Nilpotent group — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …   Wikipedia

• K-homology — In mathematics, K homology is a homology theory on the category of compact Hausdorff spaces. It classifies the elliptic pseudo differential operators acting on the vector bundles over a space. In terms of C^* algebras, it classifies the Fredholm… …   Wikipedia

• List of group theory topics — Contents 1 Structures and operations 2 Basic properties of groups 2.1 Group homomorphisms 3 Basic types of groups …   Wikipedia