Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

A Caveat on the Isomorphism Conjecture in L -theory

A Caveat on the Isomorphism Conjecture in L -theory Abstract. The Isomorphism Conjecture of Farrell and Jones for L-theory [5] has only been formulated for LÀy and in this formulation been proved for a large class of groups, for instance for discrete cocompact subgroups of a virtually connected Lie group. The question arises whether the corresponding conjecture is true for L e for the decorations e pY hY s. We give examples showing that it fails for any of the decorations e pY hY s. The groups involved are of the shape Z 2 Â F for ®nite F. 2000 Mathematics Subject Classi®cation: 19G24. We ®rst summarize the Farrell-Jones-Conjecture for L-theory as far as needed here. We will follow the notation and setup of [6], which is di¨erent, but equivalent to the original setup in [5], [8], and slightly more convenient for our purposes. Let G be a group. A family F is a class of subgroups of G which is closed under conjugation and taking subgroups. Our main examples will be the families VC of virtually cyclic subgroups, i.e. subgroups which are either ®nite or contain Z as a normal subgroup e of ®nite index, and the family ALL of all subgroups. Let Ln for e http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

A Caveat on the Isomorphism Conjecture in L -theory

Farrell, Tom; Jones, Lowell; Lück, Wolfgang
Forum Mathematicum , Volume 14 (3) – Apr 15, 2002
Download PDF
6 pages

Loading next page...
 
/lp/de-gruyter/a-caveat-on-the-isomorphism-conjecture-in-l-theory-zN0e4FY9y0

References

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
de Gruyter
Copyright
Copyright © 2002 by Walter de Gruyter GmbH & Co. KG
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/form.2002.019
Publisher site
See Article on Publisher Site

Abstract

Abstract. The Isomorphism Conjecture of Farrell and Jones for L-theory [5] has only been formulated for LÀy and in this formulation been proved for a large class of groups, for instance for discrete cocompact subgroups of a virtually connected Lie group. The question arises whether the corresponding conjecture is true for L e for the decorations e pY hY s. We give examples showing that it fails for any of the decorations e pY hY s. The groups involved are of the shape Z 2 Â F for ®nite F. 2000 Mathematics Subject Classi®cation: 19G24. We ®rst summarize the Farrell-Jones-Conjecture for L-theory as far as needed here. We will follow the notation and setup of [6], which is di¨erent, but equivalent to the original setup in [5], [8], and slightly more convenient for our purposes. Let G be a group. A family F is a class of subgroups of G which is closed under conjugation and taking subgroups. Our main examples will be the families VC of virtually cyclic subgroups, i.e. subgroups which are either ®nite or contain Z as a normal subgroup e of ®nite index, and the family ALL of all subgroups. Let Ln for e

Journal

Forum Mathematicum – de Gruyter

Published: Apr 15, 2002

There are no references for this article.