In noncommutative geometry and related branches of mathematics, cyclic homology and cyclic cohomology are certain (co)homology theories for associative algebras which generalize the de Rham (co)homology of manifolds. These notions were independently introduced by Boris Tsygan (homology)[1] and Alain Connes (cohomology)[2] in the 1980s. These invariants have many interesting relationships with several older branches of mathematics, including de Rham theory, Hochschild (co)homology, group cohomology, and the K-theory. Contributors to the development of the theory include Max Karoubi, Yuri L. Daletskii, Boris Feigin, Jean-Luc Brylinski, Mariusz Wodzicki, Jean-Louis Loday, Victor Nistor, Daniel Quillen, Joachim Cuntz, Ryszard Nest, Ralf Meyer, and Michael Puschnigg.
^Boris L. Tsygan. Homology of matrix Lie algebras over rings and the Hochschild homology. Uspekhi Mat. Nauk, 38(2(230)):217–218, 1983. Translation in Russ. Math. Survey 38(2) (1983), 198–199.
mathematics, cyclichomology and cyclic cohomology are certain (co)homology theories for associative algebras which generalize the de Rham (co)homology of manifolds...
Hochschild homology (and cohomology) is a homology theory for associative algebras over rings. There is also a theory for Hochschild homology of certain...
infinite cyclic groups within the Farrell–Jones conjecture's context. In non-commutative geometry, Kuku's research includes entire/periodic cyclichomology and...
Tsygan, Ukrainian American mathematician, the author of the concept of cyclichomology Tsygan, a Soviet space dog Tsyganov, Russian surname This disambiguation...
of a new homology theory associated to noncommutative associative algebras and noncommutative operator algebras, namely the cyclichomology and its relations...
reduced homology is a minor modification made to homology theory in algebraic topology, motivated by the intuition that all of the homology groups of...
the cyclic category to sets. More generally a cyclic object in a category C is a contravariant functor from the cyclic category to C. Cyclichomology Simplex...
connected orientable closed manifold of dimension n, the top homology group is infinite cyclic: H n ( M ; Z ) ≅ Z {\displaystyle H_{n}(M;\mathbf {Z} )\cong...
standard finite cycles is called the cyclic category; it may be used to construct Alain Connes' cyclichomology. One may define a degree of a function...
mathematics, the homology or cohomology of an algebra may refer to Banach algebra cohomology of a bimodule over a Banach algebra Cyclichomology of an associative...
kG} is also denoted by A # G {\displaystyle A\mathop {\#} G} . The cyclichomology of Hopf smash products has been computed. However, there the smash...
of the stable mapping class group, and for developing topological cyclichomology theory. Madsen earned a candidate degree from the University of Copenhagen...
[kaʁubi]) is a French mathematician, topologist, who works on K-theory, cyclichomology and noncommutative geometry and who founded the first European Congress...
(Dixon & Mortimer 1996, p. 259). The group homology of Sn is quite regular and stabilizes: the first homology (concretely, the abelianization) is: H 1 (...
at the International Congress of Mathematicians in Kyoto (Cyclic Cohomology and K-homology). Max Planck Research Award (together with G. Kasparov), 1993...
Hochschild homology in arithmetic geometry" (PDF). Archived (PDF) from the original on 24 Dec 2020. Revisiting THH(F_p) Topological cyclichomology of the...
algebraic K-theory, cyclichomology, and Hochschild homology focuses on determining the relationships between K-theory and homology theories and exploiting...
In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated...
S2CID 118378937. with Kathryn Hess, Alexander A. Voronov: String Topology and CyclicHomology, Birkhäuser 2006 with Gunnar Carlsson: The What, Where and Why of Mathematics...
PSp4(2)'. A8 is isomorphic to PSL4(2). More obviously, A3 is isomorphic to the cyclic group Z3, and A0, A1, and A2 are isomorphic to the trivial group (which...
K-theory K(A, I), for a nilpotent ideal I, is isomorphic to relative cyclichomology HC(A, I). This theorem was a pioneering result in the area of trace...
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