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Cover: 9783540633891 | High-dimensional Knot Theory | Algebraic Surgery in Codimension 2
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High-dimensional Knot Theory
Algebraic Surgery in Codimension 2
Buch von Andrew Ranicki
Sprache: Englisch

85,70 €*

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Beschreibung
High-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.
High-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.
Zusammenfassung
none
Inhaltsverzeichnis
Algebraic 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.
Details
Erscheinungsjahr: 1998
Fachbereich: Topologie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 692
Reihe: Springer Monographs in Mathematics
Inhalt: xxxvi
646 S.
ISBN-13: 9783540633891
ISBN-10: 3540633898
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Ranicki, Andrew
Auflage: 1998
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Springer Monographs in Mathematics
Maße: 241 x 160 x 42 mm
Von/Mit: Andrew Ranicki
Erscheinungsdatum: 06.08.1998
Gewicht: 1,191 kg
preigu-id: 106848404
Zusammenfassung
none
Inhaltsverzeichnis
Algebraic 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.
Details
Erscheinungsjahr: 1998
Fachbereich: Topologie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 692
Reihe: Springer Monographs in Mathematics
Inhalt: xxxvi
646 S.
ISBN-13: 9783540633891
ISBN-10: 3540633898
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Ranicki, Andrew
Auflage: 1998
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Springer Monographs in Mathematics
Maße: 241 x 160 x 42 mm
Von/Mit: Andrew Ranicki
Erscheinungsdatum: 06.08.1998
Gewicht: 1,191 kg
preigu-id: 106848404
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