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OverviewHigh-dimensional knot theory is the study of the embeddings of n-dimensional manifolds in (n+2)-dimensional manifolds, generalizing the traditional study of knots in the case n=1. The main theme is the application of the author's algebraic theory of surgery to provide a unified treatment of the invariants of codimension 2 embeddings, generalizing the Alexander polynomials and Seifert forms of classical knot theory. Many results in the research literature are thus brought into a single framework, and new results are obtained. The treatment is particularly effective in dealing with open books, which are manifolds with codimension 2 submanifolds such that the complement fibres over a circle. The book concludes with an appendix by E. Winkelnkemper on the history of open books. Full Product DetailsAuthor: E. Winkelnkemper , Andrew RanickiPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: Softcover reprint of hardcover 1st ed. 1998 Dimensions: Width: 15.50cm , Height: 3.40cm , Length: 23.50cm Weight: 1.038kg ISBN: 9783642083297ISBN 10: 3642083293 Pages: 646 Publication Date: 15 December 2010 Audience: Professional and scholarly , Professional and scholarly , Professional & Vocational , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsAlgebraic K-theory.- Finite structures.- Geometric bands.- Algebraic bands.- Localization and completion in K-theory.- K-theory of polynomial extensions.- K-theory of formal power series.- Algebraic transversality.- Finite domination and Novikov homology.- Noncommutative localization.- Endomorphism K-theory.- The characteristic polynomial.- Primary K-theory.- Automorphism K-theory.- Witt vectors.- The fibering obstruction.- Reidemeister torsion.- Alexander polynomials.- K-theory of Dedekind rings.- K-theory of function fields.- Algebraic L-theory.- Algebraic Poincaré complexes.- Codimension q surgery.- Codimension 2 surgery.- Manifold and geometric Poincaré bordism of X × S 1.- L-theory of Laurent extensions.- Localization and completion in L-theory.- Asymmetric L-theory.- Framed codimension 2 surgery.- Automorphism L-theory.- Open books.- Twisted doubles.- Isometric L-theory.- Seifert and Blanchfield complexes.- Knot theory.- Endomorphism L-theory.- Primary L-theory.- Almost symmetric L-theory.- L-theory of fields and rational localization.- L-theory of Dedekind rings.- L-theory of function fields.- The multisignature.- Coupling invariants.- The knot cobordism groups.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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