Titlebook: High-dimensional Knot Theory; Algebraic Surgery in Andrew Ranicki Book 1998 Springer-Verlag Berlin Heidelberg 1998 K-theory.homology.knots.

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Book 1998udy 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 li

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Automorphism ,-theoryorrespondence will be used to express the various automorphism .-groups of . in terms of the algebraic .-groups .. (...[., ..]) of the localizations ...[., ..] inverting appropriate sets . of square matrices in .[., ..].

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Witt vectorse identified with the Witt vector determined by the Alexander polynomials. In the applications to knot theory in Chap. 33 . will be the cellular chain complex of the infinite cyclic cover of the knot complement.

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-theory of Dedekind ringsdules ..(.) and the maximal ideal structure of .. The corresponding algebraic .-theoretic expression for a chain complex with Poincaré duality will be used in Chaps. 39–42 in the computation of the high-dimensional knot cobordism groups ...

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