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Encyclopedia > Cyclic homology

In mathematics, cyclic homology is an aspect of homological algebra. It was defined in 1983 by Alain Connes as a sequence of groups written as Euclid, detail from The School of Athens by Raphael. ... Homological algebra is the branch of mathematics which studies the methods of homology and cohomology in a general setting. ... 1983 (MCMLXXXIII) was a common year starting on Saturday of the Gregorian calendar. ... Alain Connes (born April 1, 1947) is a French mathematician, currently Professor at the College de France (Paris, France), IHES (Bures-sur-Yvette, France) and Vanderbilt University (Nashville, Tennessee). ...

HCn(R).

It may be generally defined as a certain general procedure to associate a cyclic sequence of abelian groups or modules to a given mathematical object (such as a topological space or a group). In mathematics, a sequence is a list of objects (or events) arranged in a linear fashion, such that the order of the members is well defined and significant. ... In mathematics, an abelian group, also called a commutative group, is a group (G, *) such that a * b = b * a for all a and b in G. Abelian groups are named after Niels Henrik Abel. ... In abstract algebra, the notion of a module over a ring is the common generalizations of two of the most important notions in algebra, vector space (where we take the ring to be a particular field), and abelian group (where we take the ring to be the ring of integers). ... Topological spaces are structures that allow one to formalize concepts such as convergence, connectedness and continuity. ... In mathematics, a group is a set, together with a binary operation, such as multiplication or addition, satisfying certain axioms, detailed below. ...


See also

  • Homology
  • Homology theory

In mathematics (especially algebraic topology and abstract algebra), homology (in Greek homos = identical) is a certain general procedure to associate a sequence of abelian groups or modules to a given mathematical object (such as a topological space or a group). ... In mathematics, homology theory is the axiomatic study of the intuitive geometric idea of homology of cycles on topological spaces. ...

External links

  • A personal note on Hochschild and Cyclic homology

  Results from FactBites:
 
Cyclic homology - Wikipedia, the free encyclopedia (92 words)
In mathematics, cyclic homology is an aspect of homological algebra.
It was defined in 1983 by Allan Connes, as a sequence of groups written as
It may be generally defined as a certain general procedure to associate a cyclic sequence of abelian groups or modules to a given mathematical object (such as a topological space or a group).
  More results at FactBites »


 

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