By Joachim Cuntz, Georges Skandalis, Boris Tsygan

This quantity comprises contributions by means of 3 authors and treats facets of noncommutative geometry which are regarding cyclic homology. The authors provide particularly whole debts of cyclic thought from diversified and complementary issues of view. The connections among topological (bivariant) K-theory and cyclic conception through generalized Chern-characters are mentioned intimately. This comprises an overview of a framework for bivariant K-theory on a class of in the neighborhood convex algebras. nevertheless, cyclic conception is the typical environment for various basic index theorems. A survey of such index theorems (including the summary index theorems of Connes-Moscovici and of Bressler-Nest-Tsygan) is given and the strategies and ideas enthusiastic about the evidence of those theorems are defined.

**Read Online or Download Cyclic Homology in Non-Commutative Geometry PDF**

**Similar topology books**

**Fundamental Groups and Covering Spaces **

The common personality of primary teams and masking areas are offered as compatible for introducing algebraic topology. the 2 themes are handled in separate sections. the point of interest is at the use of algebraic invariants in topological difficulties. functions to different components of arithmetic equivalent to genuine research, complicated variables, and differential geometry also are mentioned.

**Nonabelian Algebraic Topology: Filtered Spaces, Crossed Complexes, Cubical Homotopy Groupoids**

The most subject of this e-book is that using filtered areas instead of simply topological areas permits the advance of simple algebraic topology by way of better homotopy groupoids; those algebraic constructions larger mirror the geometry of subdivision and composition than these ordinarily in use.

**Conference on Algebraic Topology in Honor of Peter Hilton**

This ebook, that is the complaints of a convention held at Memorial college of Newfoundland, August 1983, includes 18 papers in algebraic topology and homological algebra by means of collaborators and co-workers of Peter Hilton. it truly is devoted to Hilton at the social gathering of his sixtieth birthday. a few of the issues lined are homotopy idea, $H$-spaces, team cohomology, localization, classifying areas, and Eckmann-Hilton duality.

- General topology
- Felix Hausdorff - Gesammelte Werke Band III: Mengenlehre (1927,1935) Deskripte Mengenlehre und Topologie (German and English Edition) (v. 3)
- Geometric Topology
- Braids and coverings
- Set Theory: Techniques and Applications. Curaçao 1995 and Barcelona 1996 Conferences

**Extra resources for Cyclic Homology in Non-Commutative Geometry**

**Sample text**

The c o n j u g a t i o n i s g i v e n by BE(T) ~ D E ( [ - 1 ] E T ) . (e) The d i a g o n a l i s g i v e n by BE(T) ~ BE(T) ~ D E ( T ) . (f) The identity Proof if BE(T) = e wl°gET by d e m o n s t r a t i n g deg f = 0, shown f o r then ( b ) by i n d u c t i o n f(w) = f(0) deg f < n holds in that there E* ® Q [ [ T ] ] , on deg f , and we s e t ~ where f o r feA E. = 1. e x = r x n n! Clearly Now s u p p o s e t h a t we h a v e is a unique E. expansion f(w) = Let E 7iDa. i

21) ring, b 0 of H0(P(V);~) and that the defining map in homology. in particular, isomorphism and the ring structure, zk(H,(P(V);~)) as Pontrjagin with the generator Z*(H,(P(V) ;2)) [b~ I], it is elementary on n and k using induces fact that H,(~U(V);~), algebra on H,(P(V);~) PV = z 6 Sn(V) ''' ~ z -rSk+rn(V) for each k > 0. 10) ~ ... 10). 23) then there will be an equivariant Sk(V ) + The theorem but not yet equivariantly. 21) gives 52 References I. F. Atiyah, K-Theory (Benjamin, 2. C. Crabb, ~ / 2 - H o m o t 0 p y 1980).

Rs ii Then g i = < ( e x p E D) i , ~E/3E> r = <(exp E (D~ s 1 + I•D)) i, t3E ®DE> =