cohomological group

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• Cohomological dimension — In abstract algebra, cohomological dimension is an invariant which measures the homological complexity of representations of a group. It has important applications in geometric group theory, topology, and algebraic number theory. Contents 1… …   Wikipedia

• 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

• Secondary calculus and cohomological physics — In mathematics, secondary calculus is a proposed expansion of classical differential calculus on manifolds, to the space of solutions of a (nonlinear) partial differential equation. It is a sophisticated theory at the level of jet spaces and… …   Wikipedia

• Tate cohomology group — In mathematics, Tate cohomology groups are a slightly modified form of the usual cohomology groups of a finite group that combine homology and cohomology groups into one sequence. They were invented by John Tate, and are used in class field… …   Wikipedia

• Geometric group theory — is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups act (that is, when the… …   Wikipedia

• Parafree group — In mathematics, in the realm of group theory, a group is said to be parafree if its quotients by the terms of its lower central series are the same as those of a free group and if it is residually nilpotent (the intersection of the terms of its… …   Wikipedia

• Artin reciprocity law — The Artin reciprocity law, established by Emil Artin in a series of papers (1924; 1927; 1930), is a general theorem in number theory that forms a central part of the global class field theory.[1] The term reciprocity law refers to a long line of… …   Wikipedia

• Chow ring — In algebraic geometry, the Chow ring (named after W. L. Chow) of an algebraic variety is an algebraic geometric analogue of the cohomology ring of the variety considered as a topological space: its elements are formed out of actual subvarieties… …   Wikipedia

• Eilenberg-Ganea conjecture — The Eilenberg Ganea conjecture is a claim in algebraic topology. It was formulated by Samuel Eilenberg and Tudor Ganea in 1957, in a short, but influential paper. It states that if a group G has cohomological dimension 2, then it has a 2… …   Wikipedia

• John R. Stallings — John Robert Stallings is a mathematician known for his seminal contributions to geometric group theory and 3 manifold topology. Stallings is a Professor Emeritus in the Department of Mathematics and the University of California at Berkeley. [… …   Wikipedia

• Mayer–Vietoris sequence — In mathematics, particularly algebraic topology and homology theory, the Mayer–Vietoris sequence is an algebraic tool to help compute algebraic invariants of topological spaces, known as their homology and cohomology groups. The result is due to… …   Wikipedia