noncommutative cohomology

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• Noncommutative geometry — Not to be confused with Anabelian geometry. Noncommutative geometry (NCG) is a branch of mathematics concerned with geometric approach to noncommutative algebras, and with construction of spaces which are locally presented by noncommutative… …   Wikipedia

• Ring (mathematics) — This article is about algebraic structures. For geometric rings, see Annulus (mathematics). For the set theory concept, see Ring of sets. Polynomials, represented here by curves, form a ring under addition and multiplication. In mathematics, a… …   Wikipedia

• Cyclic homology — In homological algebra, cyclic homology and cyclic cohomology are (co)homology theories for associative algebras introduced by Alain Connes around 1980, which play an important role in his noncommutative geometry. They were independently… …   Wikipedia

• JLO cocycle — In noncommutative geometry, the JLO cocycle is a cocycle (and thus defines a cohomology class) in entire cyclic cohomology. It is a non commutative version of the classic Chern character of the conventional differential geometry. In… …   Wikipedia

• Riemann hypothesis — The real part (red) and imaginary part (blue) of the Riemann zeta function along the critical line Re(s) = 1/2. The first non trivial zeros can be seen at Im(s) = ±14.135, ±21.022 and ±25.011 …   Wikipedia

• Differential form — In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates. Differential forms provide a better[further explanation needed] definition… …   Wikipedia

• Hodge structure — In mathematics, a Hodge structure, named after W. V. D. Hodge, is an algebraic structure at the level of linear algebra, similar to the one that Hodge theory gives to the cohomology groups of a smooth and compact Kähler manifold. A mixed Hodge… …   Wikipedia

• Duality (mathematics) — In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one to one fashion, often (but not always) by means of an involution operation: if the dual… …   Wikipedia

• Drinfel'd module — In mathematics, a Drinfel d module (or elliptic module) is roughly a special kind of module over a ring of functions on a curve over a finite field, generalizing the Carlitz module. Loosely speaking, they provide a function field analogue of… …   Wikipedia

• Alexander Grothendieck — User:Geometry guy/InfoboxAlexander Grothendieck (born March 28, 1928 in Berlin, Germany) is considered to be one of the greatest mathematicians of the 20th century. He made major contributions to: algebraic topology, algebraic geometry, number… …   Wikipedia

• Alain Connes — 2004 Alain Connes (* 1. April 1947 in Draguignan bei Cannes, Frankreich) ist ein französischer Mathematiker. Inhaltsverzeichnis …   Deutsch Wikipedia