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cohomology operator

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  • Dolbeault cohomology — In mathematics, in particular in algebraic geometry and differential geometry, Dolbeault cohomology (named after Pierre Dolbeault) is an analog of de Rham cohomology for complex manifolds. Let M be a complex manifold. Then the Dolbeault… …   Wikipedia

  • De Rham cohomology — For Grothendieck s algebraic de Rham cohomology see Crystalline cohomology. In mathematics, de Rham cohomology (after Georges de Rham) is a tool belonging both to algebraic topology and to differential topology, capable of expressing basic… …   Wikipedia

  • Čech cohomology — In mathematics, specifically algebraic topology, Čech cohomology is a cohomology theory based on the intersection properties of open covers of a topological space. It is named for the mathematician Eduard Čech. Contents 1 Motivation 2… …   Wikipedia

  • Weil cohomology theory — In algebraic geometry, a subfield of mathematics, a Weil cohomology or Weil cohomology theory is a cohomology satisfying certain axioms concerning the interplay of algebraic cycles and cohomology groups. The name is in honour of André Weil. Weil… …   Wikipedia

  • L² cohomology — In mathematics, L2 cohomology is a cohomology theory for smooth non compact manifolds M with Riemannian metric. It defined in the same way as de Rham cohomology except that one uses square integrable differential forms. The notion of square… …   Wikipedia

  • Laplace operator — This article is about the mathematical operator. For the Laplace probability distribution, see Laplace distribution. For graph theoretical notion, see Laplacian matrix. Del Squared redirects here. For other uses, see Del Squared (disambiguation) …   Wikipedia

  • Affiliated operator — In mathematics, affiliated operators were introduced by Murray and von Neumann in the theory of von Neumann algebras as a technique for using unbounded operators to study modules generated by a single vector. Later Atiyah and Singer showed that… …   Wikipedia

  • Dolbeault operator — In mathematics, a Dolbeault operator on a complex manifold is the restriction of the exterior derivative to holomorphic or to antiholomorphic forms. Thus:d = partial + ar{partial}ee also*complex differential form *Dolbeault cohomology …   Wikipedia

  • Michael Atiyah — Sir Michael Atiyah Born 22 April 1929 (1929 04 22) (age 82) …   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

  • Twisted K-theory — In mathematics, twisted K theory (also called K theory with local coefficients ) is a variation on K theory, a mathematical theory from the 1950s that spans algebraic topology, abstract algebra and operator theory. More specifically, twisted K… …   Wikipedia

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