Geometry & Topology

The surgery obstruction groups of the infinite dihedral group

Francis X Connolly and James F Davis

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

surgery infinite dihedral group Gauss sums


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.

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