Noun
(mathematics) A method of contravariantly associating a family of invariant quotient groups to each algebraic or geometric object of a category, including categories of geometric and algebraic objects.
(mathematics) A system of quotient groups associated to a topological space.
Source: en.wiktionary.orgDe Rham showed that all of these approaches were interrelated and that, for a closed, oriented manifold, the Betti numbers derived through simplicial homology were the same Betti numbers as those derived through de Rham cohomology. Source: Internet
Michael Atiyah and Friedrich Hirzebruch (right), the creators of topological K-theory The Atiyah–Hirzebruch spectral sequence relates the ordinary cohomology of a space to its generalized cohomology theory. Source: Internet
Several results showed that the newly introduced K-theory was in some ways more powerful than ordinary cohomology theory. Source: Internet
The proof using Stokes's theorem is closely related to the proof using homology (or rather cohomology), because the form ω generates the de Rham cohomology group H n−1 (∂B) used in the cohomology proof. Source: Internet
The topological condition is again that the second real cohomology group is trivial. Source: Internet
They defined homology and cohomology as functors equipped with natural transformations subject to certain axioms (e. Source: Internet