High-dimensional Knot Theory

Algebraic Surgery in Codimension 2

Andrew Ranicki

646 pages, parution le 01/10/1998

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Résumé

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.

Contents

Preface
Introduction

Pt. 1: Algebraic K-theory

1: Finite structures
2: Geometric bands
3: Algebraic bands
4: Localization and completion in K-theory
5: K-theory of polynomial extensions
6: K-theory of formal power series
7: Algebraic transversality
8: Finite domination and Novikov homology
9: Noncommutative localization
10: Endomorphism K-theory
11: The characteristic polynomial
12: Primary K-theory
13: Automorphism K-theory
14: Witt vectors
15: The fibering obstruction
16: Reidemeister torsion
17: Alexander polynomials
18: K-theory of Dedekind rings
19: K-theory of function fields

Pt. 2: Algebraic L-theory

20: Algebraic Poincare complexes
21: Codimension q surgery
22: Codimension 2 surgery
23: Manifold and geometric Poincare bordism of X x S(superscript 1)
24: L-theory of Laurent extensions
25: Localization and completion in L-theory
26: Asymmetric L-theory
27: Framed codimension 2 surgery
28: Automorphism L-theory
29: Open books
30: Twisted doubles
31: Isometric L-theory
32: Seifert and Blanchfield complexes
33: Knot theory
34: Endomorphism L-theory
35: Primary L-theory
36: Almost symmetric L-theory
37: L-theory of fields and rational localization
38: L-theory of Dedekind rings
39: L-theory of function fields
40: The multisignature
41: Coupling invariants
42: The knot cobordism groups

Appendix: The history and applications of open books (by H. E. Winkelnkemper)
References
Index

L'auteur - Andrew Ranicki

Department of Mathematics and Statistics, University of Edinburgh

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Andrew Ranicki
Parution	01/10/1998
Nb. de pages	646
Format	16 x 24
Couverture	Relié
Poids	983g
Intérieur	Noir et Blanc
EAN13	9783540633891