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...

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

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...

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

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...

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...

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

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

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

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

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

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...

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...

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

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

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

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

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

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

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

dynamical systems theory, topological field theories, stochastic differential equations (SDE), and the theory of pseudo-Hermitian operators. It can be seen...

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...

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

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

theory. Together with his advisor Emil Artin, Tate gave a cohomological treatment of global class field theory using techniques of group cohomology applied...

construct more general and refined cohomology theories to tackle the Weil conjectures. The problem was that the cohomology of a coherent sheaf over a finite...

other new SPT states protected by other symmetries. A list of bosonic SPT states from group cohomology H d + 1 [ G , U ( 1 ) ] ⊕ k = 1 d H k [ G , i T O d...

'non-commutative' theories which extend first cohomology as torsors (important in Galois cohomology). In the context of group theory, a sequence G 0 →...