cohomology
Noun
Meaning
(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.orgPhrases with the word
Examples
De 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.
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.
Several results showed that the newly introduced K-theory was in some ways more powerful than ordinary cohomology theory.
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.
The topological condition is again that the second real cohomology group is trivial.
They defined homology and cohomology as functors equipped with natural transformations subject to certain axioms (e.