Geometry & Topology

The surgery obstruction groups of the infinite dihedral group

Francis X Connolly and James F Davis

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Abstract

This paper computes the quadratic Witt groups (the Wall L–groups) of the polynomial ring [t] and the integral group ring of the infinite dihedral group, with various involutions. We show that some of these groups are infinite direct sums of cyclic groups of order 2 and 4. The techniques used are quadratic linking forms over [t] and Arf invariants.

Article information

Source
Geom. Topol., Volume 8, Number 3 (2004), 1043-1078.

Dates
Received: 5 June 2003
Accepted: 11 July 2004
First available in Project Euclid: 21 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513883462

Digital Object Identifier
doi:10.2140/gt.2004.8.1043

Mathematical Reviews number (MathSciNet)
MR2087078

Zentralblatt MATH identifier
1052.57049

Subjects
Primary: 57R67: Surgery obstructions, Wall groups [See also 19J25]
Secondary: 19J25: Surgery obstructions [See also 57R67] 19G24: $L$-theory of group rings [See also 11E81]

Keywords
surgery infinite dihedral group Gauss sums

Citation

Connolly, Francis X; Davis, James F. The surgery obstruction groups of the infinite dihedral group. Geom. Topol. 8 (2004), no. 3, 1043--1078. doi:10.2140/gt.2004.8.1043. https://projecteuclid.org/euclid.gt/1513883462


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