extraordinary cohomology
1Cohomology — In mathematics, specifically in algebraic topology, cohomology is a general term for a sequence of abelian groups defined from a co chain complex. That is, cohomology is defined as the abstract study of cochains, cocycles, and coboundaries.… …
2Cohomology operation — In mathematics, the cohomology operation concept became central to algebraic topology, particularly homotopy theory, from the 1950s onwards, in the shape of the simple definition that if F is a functor defining a cohomology theory, then a… …
3List of cohomology theories — 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 categories of CW complexes or spectra. For other sorts of homology theories see the links at… …
4Cobordism — A cobordism (W;M,N). In mathematics, cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary of a manifold. Two manifolds are cobordant if their disjoint… …
5Spectral sequence — In the area of mathematics known as homological algebra, especially in algebraic topology and group cohomology, a spectral sequence is a means of computing homology groups by taking successive approximations. Spectral sequences are a… …
6Atiyah–Hirzebruch spectral sequence — In mathematics, the Atiyah–Hirzebruch spectral sequence is a computational tool from homological algebra, designed to make possible the calculation of an extraordinary cohomology theory. For a CW complex X , or more general topological space, it… …
7Eilenberg–Steenrod axioms — In mathematics, specifically in algebraic topology, the Eilenberg–Steenrod axioms are properties that homology theories of topological spaces have in common. The quintessential example of a homology theory satisfying the axioms is singular… …
8Mayer–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… …
9K-theory — In mathematics, K theory is a tool used in several disciplines. In algebraic topology, it is an extraordinary cohomology theory known as topological K theory. In algebra and algebraic geometry, it is referred to as algebraic K theory. It also has …
10Eilenberg-Steenrod axioms — In mathematics, specifically in algebraic topology, the Eilenberg Steenrod axioms are properties that homology theories of topological spaces have in common. The quintessential example of a homology theory satisfying the axioms is singular… …
