@MISC{Reich05londonparis, author = {Holger Reich}, title = {London Paris Tokyo HongKong Barcelona Budapest Preface}, year = {2005} }

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Abstract

Comment 1 (By W.): Here the main preface has to be inserted. Comment 2 (By W.): Shall we insert a general list of criteria why it is worthwhile to study a conjecture. A User’s Guide Comment 3 (ByW.): This paragraph has to be adjusted and completed. A reader who wants to get specific information or focus on a certain topic should consult the detailed table of contents, the index and the index of notation in order to find the right place in the paper. We have tried to write the text in a way such that one can read small units independently from the rest. Moreover, a reader who may only be interested in the Baum-Connes Conjecture or only in the Farrell-Jones Conjecture for K-theory or for L-theory can ignore the other parts. But we emphasize again that one basic idea of this paper is to explain the parallel treatment of these conjectures. A reader without much prior knowledge about the Baum-Connes Con-jecture or the Farrell-Jones Conjecture should begin with Chapter 1. There, the special case of a torsionfree group is treated, since the formulation of the conjectures is less technical in this case and there are already many interest-ing applications. The applications are not needed later. A more experienced reader may pass directly to Chapter 2. Other (survey) articles on the Farrell-Jones Conjecture and the Baum-Connes Conjecture are [126], [143], [163], [226], [246], [335]. We require that the reader is familiar with basic notions in topology (CW-complexes, chain complexes, homology, homotopy groups, manifolds, cover-ings), functional analysis (Hilbert spaces, bounded operators, differential op-erators, C∗-algebras), and algebra (groups, modules, elementary homological algebra). Comment 4 (By W.): This list is not yet complete.