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? TheconferenceC -algebrasandelliptic theory,II  washeldattheStefanBanach International Mathematical Center in Bed ¸ lewo, Poland, in January 2006, one of a series of meetings in Polandand Russia. This volumeis a collectionof originaland refereed researchand expositorypapers related to the meeting. Although centered on the K-theory of operator algebras, a broad range of topics is covered including 2 geometric, L - and spectral invariants, such as the analytic torsion, signature and index, of di?erential and pseudo-di?erential operators on spaces which are pos- bly singular, foliated or non-commutative. This material should be of interest to researchers in Mathematical Physics, Di?erential Topology and Analysis. The series of conferences including this one originatedwith an idea of Prof- sorBogdanBojarski,namely,tostrengthencollaborationbetweenmathematicians from Poland and Russia on the basis of common scienti?c interests, particularly in the ?eld of Non-commutative Geometry. This led to the ?rst meeting, in 2004, whichbroughttogetherabout60mathematiciansnotonlyfromRussiaandPoland, but from other leading centers. It was supported by the European program G- metric Analysis Research Training Network . Since then there have been annual meetings alternating between B¸ edlewo and Moscow. The second conference was organized in Moscow in 2005 and was dedicated to the memory of Yu.P. Solovyov. The proceedings will appear in the Journal of K-Theory. The conference on which this volume is based was the third conference in the overall series with the fourth being held in Moscow in 2007. A further meeting in Bed ¸ lewo is planned for 2009.

Functional analysis --- functies (wiskunde)