homology group
81Duality (mathematics) — In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one to one fashion, often (but not always) by means of an involution operation: if the dual… …
82Stokes' theorem — For the equation governing viscous drag in fluids, see Stokes law. Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus  Derivative Change of variables Implicit differentiatio …
83Moore space (algebraic topology) — See also Moore space for other meanings in mathematics. In algebraic topology, a branch of mathematics, Moore space is the name given to a particular type of topological space that is the homology analogue of the Eilenberg–Maclane spaces of… …
84Zig-zag lemma — In mathematics, particularly homological algebra, the zig zag lemma asserts the existence of a particular long exact sequence in the homology groups of certain chain complexes. The result is valid in every abelian category. Statement In an… …
85Lagrangian Grassmannian — In mathematics, the Lagrangian Grassmannian is the smooth manifold of Lagrangian subspaces of a real symplectic vector space V. Its dimension is n(n+1)/2 (where the dimension of V is 2n). It may be identified with the homogeneous space U(n)/O(n)… …
86Combinatorial topology — In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when topological invariants of spaces (for example the Betti numbers) were regarded as derived from combinatorial decompositions such as… …
87Hodge cycle — In mathematics, a Hodge cycle is a particular kind of homology class defined on a complex algebraic variety V , or more generally on a Kähler manifold. A homology class x in a homology group : H k ( V , C ) = H where V is a non singular complex… …
88Lefschetz duality — In mathematics, Lefschetz duality is a version of Poincaré duality in geometric topology, applying to a manifold with boundary. Such a formulation was introduced by Solomon Lefschetz in the 1920s, at the same time introducing relative homology,… …
89Seifert-Weber space — In mathematics, Seifert Weber space is a closed hyperbolic 3 manifold. It is also known as Seifert Weber dodecahedral space and hyperbolic dodecahedral space. It is one of the first discovered examples of closed hyperbolic 3 manifolds.To… …
90Commutator subgroup — In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group.[1][2] The commutator subgroup is important because it is the smallest… …
