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The Algebraic Theory of Surgery I. Foundations
Author(s) -
Ranicki Andrew
Publication year - 1980
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-40.1.87
Subject(s) - citation , mathematics , algebraic number , algebra over a field , library science , computer science , pure mathematics , mathematical analysis
algebra. An n-dimensional algebraic Poincare complex over a ring A with an involution -: A -+ A; a r+ a is an A-module chain complex G with an n-dimensional Poincare duality H*(G) = Hn_*(G). We shall use n-dimensional algebraic Poincare complexes to define two sequences of covariant functors Ln {Ln}: (rings with involution) -+ (abelian groups) (n E Z) . such that LO(A) {respectively Lo(A)} is the Witt group of non-singular symmetric {quadratic} forms over A. The quadratic L-groups Ln(A) will turn out to be the surgery obstruction groups of Wall [25], with a 4-periodicity