The surgery obstruction groups of the infinite dihedral group

Connolly, Francis X; Davis, James F

doi:10.2140/gt.2004.8.1043

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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

DOI: 10.2140/gt.2004.8.1043

arXiv: math.GT/0306054

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

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

Volume 8, issue 3 (2004)