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rational cohomology class

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  • Class formation — In mathematics, a class formation is a structure used to organize the various Galois groups and modules that appear in class field theory. They were invented by Emil Artin and John Tate. Contents 1 Definitions 2 Examples of class formations 3 The …   Wikipedia

  • Class field theory — In mathematics, class field theory is a major branch of algebraic number theory that studies abelian extensions of number fields. Most of the central results in this area were proved in the period between 1900 and 1950. The theory takes its name… …   Wikipedia

  • Chern class — In mathematics, in particular in algebraic topology and differential geometry, the Chern classes are characteristic classes associated to complex vector bundles. Chern classes were introduced by Shiing Shen Chern (1946). Contents 1 Basic… …   Wikipedia

  • Pontryagin class — In mathematics, the Pontryagin classes are certain characteristic classes. The Pontryagin class lies in cohomology groups with index a multiple of four. It applies to real vector bundles. Definition Given a vector bundle E over M , its k th… …   Wikipedia

  • Mapping class group — In mathematics, in the sub field of geometric topology, the mapping class group is an important algebraic invariant of a topological space. Briefly, the mapping class group is a discrete group of symmetries of the space. Contents 1 Motivation 2… …   Wikipedia

  • Fujiki class C — In algebraic geometry, a complex manifold is called Fujiki class C if it is bimeromorphic to a compact Kähler manifold. This notion was defined by Akira Fujiki. [A. Fujiki, On Automorphism Groups of Compact Kähler Manifolds, Inv. Math. 44 (1978)… …   Wikipedia

  • List 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… …   Wikipedia

  • Hodge conjecture — The Hodge conjecture is a major unsolved problem in algebraic geometry which relates the algebraic topology of a non singular complex algebraic variety and the subvarieties of that variety. More specifically, the conjecture says that certain de… …   Wikipedia

  • Chow ring — In algebraic geometry, the Chow ring (named after W. L. Chow) of an algebraic variety is an algebraic geometric analogue of the cohomology ring of the variety considered as a topological space: its elements are formed out of actual subvarieties… …   Wikipedia

  • Gromov–Witten invariant — In mathematics, specifically in symplectic topology and algebraic geometry, Gromov–Witten (GW) invariants are rational numbers that, in certain situations, count pseudoholomorphic curves meeting prescribed conditions in a given symplectic… …   Wikipedia

  • Atiyah–Singer index theorem — In the mathematics of manifolds and differential operators, the Atiyah–Singer index theorem states that for an elliptic differential operator on a compact manifold, the analytical index (closely related to the dimension of the space of solutions) …   Wikipedia

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