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 $ℤ\left[t\right]$ 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 $ℤ\left[t\right]$ and Arf invariants.

Keywords
surgery, infinite dihedral group, Gauss sums
Mathematical Subject Classification 2000
Primary: 57R67
Secondary: 19J25, 19G24