This volume contains the proceedings of the conference on "C*-algebras and Elliptic Theory" held in Bedlewo, Poland, in February 2004. It consists of original research papers and expository articles focussing on index theory and topology of manifolds.

The collection offers a cross-section of significant recent advances in several fields, the main subject being K-theory (of C*-algebras, equivariant K-theory). A number of papers is related to the index theory of pseudodifferential operators on singular manifolds (with boundaries, corners) or open manifolds. Further topics are Hopf cyclic cohomology, geometry of foliations, residue theory, Fredholm pairs and others. The wide spectrum of subjects reflects the diverse directions of research emanating from the Atiyah-Singer index theorem.

Contributors:

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, K. Thomsen, E.V. Troitsky, E. Vasseli, A. Weber

Zusammenfassung

This book consists of reviewed original research papers and expository articles in index theory (especially on singular manifolds), topology of manifolds, operator and equivariant K-theory, Hopf cyclic cohomology, geometry of foliations, residue theory, Fredholm pairs and others, and applications in mathematical physics. The wide spectrum of subjects reflects the diverse directions of research for which the starting point was the Atiyah-Singer index theorem.

Inhalt
Correspondences and Index.- Approximation Properties for Discrete Groups.- A Riemannian Invariant, Euler Structures and Some Topological Applications.- Morse Inequalities for Foliations.- Index Theory for Generalized Dirac Operators on Open Manifolds.- Semiclassical Asymptotics and Spectral Gaps for Periodic Magnetic Schrödinger Operators on Covering Manifolds.- The Group of Unital C*-extensions.- Lefschetz Theory on Manifolds with Singularities.- Residues and Index for Bisingular Operators.- On the Hopf-type Cyclic Cohomology with Coefficients.- The Thom Isomorphism in Gauge-equivariant K-theory.- Pseudodifferential Subspaces and Their Applications in Elliptic Theory.- New L 2-invariants of Chain Complexes and Applications.- Bundles of C*-algebras and the KK(X;?,?)-bifunctor.