homology group
21Reduced homology — In mathematics, reduced homology is a minor modification made to homology theory in algebraic topology, designed to make a point have all its homology groups zero. This change is required to make statements without some number of exceptional… …
22Superperfect group — In mathematics, in the realm of group theory, a group is said to be superperfect when its first two homology groups are trivial.The first homology group of a group is the abelianization of the group itself, since the homology of a group G is the… …
23Relative homology — In algebraic topology, a branch of mathematics, the (singular) homology of a topological space relative to a subspace is a construction in singular homology, for pairs of spaces. The relative homology is useful and important in several ways.… …
24Coxeter 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 …
25Binary icosahedral group — In mathematics, the binary icosahedral group is an extension of the icosahedral group I of order 60 by a cyclic group of order 2. It can be defined as the preimage of the icosahedral group under the 2:1 covering homomorphism:mathrm{Sp}(1) o… …
26Alternating group — In mathematics, an alternating group is the group of even permutations of a finite set. The alternating group on the set {1,..., n } is called the alternating group of degree n , or the alternating group on n letters and denoted by A n or Alt( n… …
27Homotopy group — In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The base point preserving maps from an n dimensional sphere (with base point) into a given space (with base point) are collected into equivalence… …
28Cellular homology — In mathematics, cellular homology in algebraic topology is a homology theory for CW complexes. It agrees with singular homology, and can provide an effective means of computing homology modules. If X is a CW complex with n skeleton Xn , the… …
29Compactly-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… …
30Pushforward (homology) — Let X and Y be two topological spaces and f:X ightarrow Y a continuous function. Then f induces a homomorphism between the homology groups f {*}:H nleft(X ight) ightarrow H nleft(Y ight) for ngeq0. We say that f {*} is the pushforward induced by… …
