The surgery obstruction groups of the infinite dihedral group

Connolly, Francis X¹ ; Davis, James F²

¹ Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, USA
² Department of Mathematics, Indiana University, Bloomington, Indiana 47405, USA

Geometry & topology, Tome 8 (2004) no. 3, pp. 1043-1078.

Résumé

This paper computes the quadratic Witt groups (the Wall $L$–groups) of the polynomial ring $\mathbb{Z}\left[t\right]$ 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 $\mathbb{Z}\left[t\right]$ and Arf invariants.

Détail

DOI : 10.2140/gt.2004.8.1043

Keywords: surgery, infinite dihedral group, Gauss sums

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