C*-algebras and Elliptic Theory by Bogdan Bojarski, Alexander S. Mishchenko, Evgenij V.

By Bogdan Bojarski, Alexander S. Mishchenko, Evgenij V. Troitsky, Andrzej Weber, Dan Burghelea, Richard Melrose, Victor Nistor

This quantity comprises the lawsuits of the convention on "C*-algebras and Elliptic idea" held in Bedlewo, Poland, in February 2004. It includes unique examine papers and expository articles focussing on index idea and topology of manifolds.

The assortment bargains a cross-section of vital fresh advances in different fields, the most topic being K-theory (of C*-algebras, equivariant K-theory). a couple of papers is expounded to the index concept of pseudodifferential operators on singular manifolds (with barriers, corners) or open manifolds. additional subject matters are Hopf cyclic cohomology, geometry of foliations, residue concept, Fredholm pairs and others. The vast spectrum of matters displays the varied instructions of study emanating from the Atiyah-Singer index theorem.


B. Bojarski, J. Brodzki, D. Burghelea, A. Connes, J. Eichhorn, T. Fack, S. Haller, Yu.A. Kordyukov, V. Manuilov, V. Nazaikinskii, G.A. Niblo, F. Nicola, I.M. Nikonov, V. Nistor, L. Rodino, A. Savin, V.V. Sharko, G.I. Sharygin, B. Sternin, okay. Thomsen, E.V. Troitsky, E. Vasseli, A. Weber


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Extra resources for C*-algebras and Elliptic Theory

Example text

Consider a section X of p∗ T M which is 44 D. Burghelea and S. Haller transversal to the zero section and which restricts to Xi on {i} × M , i = 1, 2. The zero set X−1 (0) is a closed one-dimensional canonically oriented submanifold of I × M . Hence it defines a homology class in I × M , which turns out to be independent of the chosen homotopy X. We thus define cs(X1 , X2 ) := p∗ (X−1 (0)) ∈ H1 (M ; Z). One can show that R(X2 , g, ω) − R(X1 , g, ω) = ω. cs(X1 ,X2 ) This property will be verified below in a slightly more general situation.

French) Bull. Soc. Math. France 92 (1964), 181–236. [6] J. Faraut and K. Harzallah, Distances hilbertiennes invariantes sur un espace homog`ene. Ann. Inst. Fourier (Grenoble) 24 (1974), no. 3, xiv, 171–217. [7] A. Grothendieck, Produits tensoriels topologiques et espaces nucl´eaires. Mem. Amer. Math. Soc. (1955), no. 16, 140 pp. [8] U. Haagerup, An example of a non-nuclear C ∗ -algebra which has the metric approximation property. Inventiones Math. 50 (1979), 279–293. Approximation Properties 35 [9] U.

Brodzki would like to thank the organizers for providing a very stimulating environment for exchanging ideas. 2. Algebras associated with groups It is well known that all topological information about a compact Hausdorff space X can be recovered from the unital abelian C ∗ -algebra C(X) of continuous functions on X. Moreover, it is known that any commutative C ∗ -algebra is isomorphic to an algebra of continuous functions on a locally compact space X. This point of view has been developed with great success within noncommutative geometry, which provides the geometric, analytic and homological tools for the study of ‘quantum spaces’.

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