http://toknotes.mimuw.edu.pl/sem5/files/Wodzicki_cht_1.pdf

Cyclic Homology Theory, Part II

http://toknotes.mimuw.edu.pl/sem5/files/Loday_cht_2.pdf

Part I:
One way of discovering the cyclic (co)homology theory is to unravel completely the most simple simplicial model of the circle. Comparing its simplicial structure with the n-stratum (identified with the cyclic group of order n+1) gives right away the construction of the cyclic category. Then follows the definition of a cyclic module and all its (co)homology theories: simplicial, cyclic, negative cyclic, periodic. Then, one can apply them to different kinds of cyclic modules: among the most important ones are those which come from an associative algebra and those which come from a Hopf algebra. On the topological side, cyclic spaces give rise to topological spaces equipped with an action of the circle. The Chern character, which, historically, was the motivation for Alain Connes to set up the cyclic cohomology theory, permits us to compare algebraic K-theory to cyclic homology.

Part II:
This part is concerned with some more advanced computations. A detailed calculation of symbols, and of the algebra of pseudodifferential operators (of unbounded order as well as of order zero) will be presented. Connections with the noncommutative residue, the higher noncommutative residue, and the Virasoro cocycle will be described.





Cyclic Homology Theory, Part II

http://toknotes.mimuw.edu.pl/sem5/files/Loday_cht_2.pdf