Volume 8, issue 3 (2004)

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The surgery obstruction groups of the infinite dihedral group

Francis X Connolly and James F Davis

Geometry & Topology 8 (2004) 1043–1078

arXiv: math.GT/0306054

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.

Keywords
surgery, infinite dihedral group, Gauss sums
Mathematical Subject Classification 2000
Primary: 57R67
Secondary: 19J25, 19G24
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Publication
Received: 5 June 2003
Accepted: 11 July 2004
Published: 18 August 2004
Proposed: Steven Ferry
Seconded: Benson Farb, Ralph Cohen
Authors
Francis X Connolly
Department of Mathematics
University of Notre Dame
Notre Dame
Indiana 46556
USA
James F Davis
Department of Mathematics
Indiana University
Bloomington
Indiana 47405
USA