Algebraic & Geometric Topology

$K$–theory of virtually poly-surface groups

S K Roushon

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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.

Article information

Source
Algebr. Geom. Topol., Volume 3, Number 1 (2003), 103-116.

Dates
Received: 25 April 2002
Revised: 15 January 2003
Accepted: 7 February 2003
First available in Project Euclid: 21 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513882369

Digital Object Identifier
doi:10.2140/agt.2003.3.103

Mathematical Reviews number (MathSciNet)
MR1997315

Zentralblatt MATH identifier
1037.19002

Subjects
Primary: 19B28: $K_1$of group rings and orders [See also 57Q10] 19A31: $K_0$ of group rings and orders 20F99: None of the above, but in this section 19D35: Negative $K$-theory, NK and Nil
Secondary: 19J10: Whitehead (and related) torsion

Keywords
strongly poly-free groups poly-closed surface groups Whitehead group fibered isomorphism conjecture

Citation

Roushon, S K. $K$–theory of virtually poly-surface groups. Algebr. Geom. Topol. 3 (2003), no. 1, 103--116. doi:10.2140/agt.2003.3.103. https://projecteuclid.org/euclid.agt/1513882369


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References

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