The isomorphism conjecture in L-theory

Details The isomorphism conjecture in L-theory The isomorphism conjecture in L-theory

2007-03-29

arxiv.org/abs/math/0703879v4

Topology Appl. 157 (2010) 508-515

Mathematics

K-Theory and Homology

14 pages, AMSLATEX file, the title is revised. item 3 in theorem 1.3 is removed as the proof of this item was found incorrect

Scientific paper

10.1016/j.topol.2009.10.012

This is the first of three articles on the Fibered Isomorphism Conjecture of Farrell and Jones for L-theory. We apply the general techniques developed in [15] and [16] to the L-theory case of the conjecture and prove several results. Here we prove the conjecture, after inverting 2, for poly-free groups. In particular, it follows for braid groups. We also prove the conjecture for some classes of groups without inverting 2. In fact we consider a general class of groups satisfying certain conditions which includes the above groups and some other important classes of groups. We check that the properties we defined in [15] are satisfied in several instances of the conjecture.

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