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

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

The assortment bargains a cross-section of vital contemporary advances in different fields, the most topic being K-theory (of C*-algebras, equivariant K-theory). a few papers is expounded to the index thought of pseudodifferential operators on singular manifolds (with barriers, corners) or open manifolds. extra subject matters are Hopf cyclic cohomology, geometry of foliations, residue thought, Fredholm pairs and others. The extensive spectrum of topics displays the various instructions of study 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, okay. Thomsen, E.V. Troitsky, E. Vasseli, A. Weber

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This condition ensures (among many other things) that the space is uniquely geodesic and contractible. Now according to Niblo and Reeves [19] given a group acting on a CAT(0) cube complex we obtain a conditionally negative kernel on the group which gives rise to a conditionally negative length function. By results of Chatterji and Ruane [3] the group will have the rapid decay property with respect to this this length function provided that the action is properly discontinuous, stabilisers are uniformly bounded and the cube complex has ﬁnite dimension.

Springer Verlag, Berlin 1999. [2] I. Chatterji, Property (RD) for cocompact lattices in a ﬁnite product of rank one Lie groups with some rank two Lie groups. Geom. Dedicata 96 (2003), 161–177. [3] I. Chatterji, K. Ruane, Some geometric groups with rapid decay. Geom. Funct. Anal. 15 (2005), no. 2, 311–339. [4] J. de Canniere, U. Haagerup, Multipliers of the Fourier algebra of some simple Lie groups and their discrete subgroups. Amer. J. Math. 107 (1984), 455–500. [5] P. Eymard, L’alg`ebre de Fourier d’un groupe localement compact.

24 J. A. Niblo of functions. A very interesting example of when this can be done is provided by the class that satisfy the rapid decay property (RD), introduced by Jolissaint [12]. Here the control on growth is derived from a length function which turns the group Γ into a metric space with interesting geometry. 1. A length function on a discrete group Γ is a function : Γ → R taking values in the non-negative reals which satisﬁes the following conditions: 1. (1) = 0, where 1 is the identity element of the group; 2.