Geometry & Topology, Vol. 8 (2004) Paper no. 29, pages 1043--1078.

The surgery obstruction groups of the infinite dihedral group

Francis X Connolly, James F Davis

Abstract. This paper computes the quadratic Witt groups (the Wall L-groups) of the polynomial ring Z[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 Z[t] and Arf invariants.

Keywords. Surgery, infinite dihedral group, Gauss sums

AMS subject classification. Primary: 57R67. Secondary: 19J25, 19G24.

DOI: 10.2140/gt.2004.8.1043

E-print: arXiv:math.GT/0306054

Submitted to GT on 5 June 2003. Paper accepted 11 July 2004. Paper published 18 August 2004.

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Francis X Connolly, James F Davis
Department of Mathematics, University of Notre Dame
Notre Dame, IN 46556, USA
and
Department of Mathematics, Indiana University
Bloomington, IN 47405, USA
Email: connolly.1@nd.edu, jfdavis@indiana.edu

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