The L-theory of twisted quadratic extensions. (English) Zbl 0635.57017

Ranicki, Andrew

Can. J. Math. 39, No. 2, 345-364 (1987).

For surgery on codimension 1 submanifolds with non-trivial normal bundle the theory of Wall has obstruction groups \(LN_*(\pi '\to \pi)\) with \(\pi\) ’ a subgroup of index 2 in \(\pi\). The main result of the present paper gives an algebraic version of the identification of \(LN_*(\pi '\to \pi)\) with \(L_*({\mathbb{Z}}[\pi '],\alpha,u)\), (\(\alpha\),u) an antistructure on \({\mathbb{Z}}[\pi ']\), valid in the more general setting of twisted quadratic extensions of rings.

Reviewer: M.Kolster

MSC:

57R67	Surgery obstructions, Wall groups
18F25	Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
57R65	Surgery and handlebodies

Keywords:

algebraic L-theory; surgery on codimension 1 submanifolds with non- trivial normal bundle; obstruction groups; twisted quadratic extensions of rings