The surgery obstruction groups of the infinite dihedral group

Francis X. Connolly, James F. Davis

Published 2003-06-03, updated 2004-09-04Version 2

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.