This is a list of some of the ordinary and generalized (or extraordinary) homology and cohomology theories in algebraic topology that are defined on the...

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

cohomology theories List of commutative algebra topics List of homological algebra topics List of group theory topics List of representation theory topics...

In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold M using partial differential...

theorem Cohomology List of cohomology theories Cocycle class Cup product Cohomology ring De Rham cohomology Čech cohomology Alexander–Spanier cohomology Intersection...

In mathematics, cohomology with compact support refers to certain cohomology theories, usually with some condition requiring that cocycles should have...

related notion of the cohomology of a cochain complex, giving rise to various cohomology theories, in addition to the notion of the cohomology of a topological...

list of mathematical theories. Almgren–Pitts min-max theory Approximation theory Arakelov theory Asymptotic theory Automata theory Bass–Serre theory Bifurcation...

often instead of using it directly one uses some slightly weaker theories derived from it, such as Brown–Peterson cohomology or Morava K-theory, that are...

study of high-dimensional manifolds, namely surgery theory. In algebraic topology, cobordism theories are fundamental extraordinary cohomology theories, and...

complex oriented cohomology theory whose associated formal group law is p-typical. List of cohomology theories#Brown–Peterson cohomology Adams, J. Frank...

topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory. Every such cohomology theory is representable,...

sought-after étale cohomology (as well as other refined theories such as flat cohomology and crystalline cohomology). At this point—about 1964—the developments powered...

topology, it is a cohomology theory known as topological K-theory. In algebra and algebraic geometry, it is referred to as algebraic K-theory. It is also a...

reduction of the cohomology), notably the Steenrod algebra structure. Since the number of homology theories has become large (see Category:Homology theory), the...

algebra? Goncharov conjecture on the cohomology of certain motivic complexes. Green's conjecture: the Clifford index of a non-hyperelliptic curve is determined...

principle Hasse–Minkowski theorem Galois module Galois cohomology Brauer group Class field theory Abelian extension Kronecker–Weber theorem Hilbert class...

K-theory and Galois cohomology. The result has a relatively elementary formulation and at the same time represents the key juncture in the proofs of many...

mathematics, Deligne–Lusztig theory is a way of constructing linear representations of finite groups of Lie type using ℓ-adic cohomology with compact support...

topology and algebraic geometry, a quantum cohomology ring is an extension of the ordinary cohomology ring of a closed symplectic manifold. It comes in...

vector cohomology Monsky–Washnitzer cohomology Infinitesimal cohomology Crystalline cohomology Rigid cohomology p-adic Hodge theory Étale cohomology, taking...

the theory has no dynamics. Instead, all observables depend on the topology of a configuration. Such theories are known as topological theories. Classically...

algebraic de Rham cohomology to complement it. Closely linked to these cohomology theories, he originated topos theory as a generalisation of topology (relevant...

1960s that many of the classical applications could be proved more easily using generalized cohomology theories, such as in his reproof of the Hopf invariant...

these cohomology theories. Some of these cohomology theories, in particular complex cobordism, turned out to be some of the most powerful cohomology theories...

geometry to string theory and related theories such as supersymmetric Yang-Mills theories in order to develop models for heterotic string theory from suitable...

Miller, Haynes (2000). "Leray in Oflag XVIIA: The origins of sheaf theory, sheaf cohomology, and spectral sequences" (ps). Archived from the original...

product of groups Direct sum of groups Extension problem Free abelian group Free group Free product Generating set of a group Group cohomology Group extension...

In mathematics, Eichler cohomology (also called parabolic cohomology or cuspidal cohomology) is a cohomology theory for Fuchsian groups, introduced by...

The following is a list of topics named after Évariste Galois (1811–1832), a French mathematician. Galois closure Galois cohomology Galois connection Galois...