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$K$–theory of virtually poly-surface groups

S K Roushon

Algebraic & Geometric Topology 3 (2003) 103–116

Erratum: Algebraic & Geometric Topology 3 (2003) 1291–1292

arXiv: math.GT/0209118

Abstract

In this paper we generalize the notion of strongly poly-free group to a larger class of groups, we call them strongly poly-surface groups and prove that the Fibered Isomorphism Conjecture of Farrell and Jones corresponding to the stable topological pseudoisotopy functor is true for any virtually strongly poly-surface group. A consequence is that the Whitehead group of a torsion free subgroup of any virtually strongly poly-surface group vanishes.

Keywords
strongly poly-free groups, poly-closed surface groups, Whitehead group, fibered isomorphism conjecture
Mathematical Subject Classification 2000
Primary: 19B28, 19A31, 20F99, 19D35
Secondary: 19J10
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Publication
Received: 25 April 2002
Revised: 15 January 2003
Accepted: 7 February 2003
Published: 8 February 2003
Authors
S K Roushon
School of Mathematics
Tata Institute
Homi Bhabha Road
Mumbai 400 005
India
http://www.math.tifr.res.in/~roushon/paper.html