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cohomology with coefficients in a fixed abelian group A, and general sheaf cohomology in which coefficients vary from point to point. Local coefficient systems...

first defined cochains. 1943 Norman Steenrod publishes on homology with local coefficients. 1945 Jean Leray publishes work carried out as a prisoner of...

cohomology or (in the case of real coefficients) De Rham cohomology. One of the ideas that led to the development of homology was the observation that certain...

specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological...

Steenrod algebra Steenrod homology Steenrod operations Steenrod problem Steenrod, Norman E. (1943). "Homology with local coefficients". Annals of Mathematics...

In topology, a branch of mathematics, intersection homology is an analogue of singular homology especially well-suited for the study of singular spaces...

Cartan & Eilenberg (1956) defined the Hochschild homology and cohomology group of A with coefficients in M in terms of the Tor functor and Ext functor...

cyclic homology and cyclic cohomology are certain (co)homology theories for associative algebras which generalize the de Rham (co)homology of manifolds...

G1 and G2, the homology of the amalgamated product G := G 1 ⋆ A G 2 {\displaystyle G:=G_{1}\star _{A}G_{2}} (with integer coefficients) lies in a long...

the point of view of homology theory. A homology G-manifold (without boundary) of dimension n over an abelian group G of coefficients is a locally compact...

manifolds; topological manifolds. There are also related classes, such as homology manifolds and orbifolds, that resemble manifolds. It took a generation...

simply connected CW complex Y together with a map from X to Y such that Y is A-local; this means that all its homology groups are modules over A The map from...

{\displaystyle f} induces an isomorphism of fundamental groups and use homology with local coefficients in Z [ π 1 ( X ) ] {\displaystyle Z[\pi _{1}(X)]} .) By Whitehead's...

Formulations applicable to general topological manifolds often employ methods of homology theory, whereas for differentiable manifolds more structure is present...

~ {\displaystyle {\tilde {H}}} stands for reduced homology or reduced cohomology, with coefficients in a given abelian group, there is an isomorphism...

{\displaystyle \varphi } induces an isomorphism on all homology groups with any local coefficient system. The Barratt–Priddy theorem implies that the space...

fH_{i}M=H_{i}M/\tau H_{i}M} be the free part – all homology groups taken with integer coefficients in this section. Then there are bilinear maps which...

sequence in singular homology for the triad (X, A, B) is a long exact sequence relating the singular homology groups (with coefficient group the integers...

cohomology groups of X with coefficients in an abelian group A are isomorphic to sheaf cohomology with constant coefficients, H*(X,AX). For example,...

agrees with singular homology with rational coefficients, whereas K(1) is a summand of mod-p complex K-theory. The theory K(n) has coefficient ring Fp[vn...