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The L-Theory of Twisted Quadratic Extensions

Published online by Cambridge University Press:  20 November 2018

Andrew Ranicki
Andrew Ranicki*
Affiliation:
University of Edinburgh, Edinburgh, Scotland
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For surgery on codimension 1 submanifolds with non-trivial normal bundle the theory of Wall [13, Section 12C] has obstruction groups LN∗(π′ → π), with π a group and π′ a subgroup of index 2, such that there is defined an exact sequence involving the ordinary L-groups of rings with involution

with the superscript w signifying a different involution on Z[π]. Geometry was used in [13] to identify

with (α, u) an antistructure on Z[π′] in the sense of Wall [14]. The main result of this paper is a purely algebraic version of this identification, for any twisted quadratic extension of a ring with antistructure.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 39 , Issue 2 , 01 April 1987 , pp. 345 - 364
Copyright
Copyright © Canadian Mathematical Society 1987

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