Shortcuts
Top of page (Alt+0)
Page content (Alt+9)
Page menu (Alt+8)
Your browser does not support javascript, some WebOpac functionallity will not be available.
.
Default
.
PageMenu
-
Main Menu
-
Simple Search
.
Advanced Search
.
Journal Search
.
Refine Search Results
.
Preferences
.
Search Menu
Simple Search
.
Advanced Search
.
New Items Search
.
Journal Search
.
Refine Search Results
.
Bottom Menu
Help
Italian
.
English
.
German
.
New Item Menu
New Items Search
.
New Items List
.
Links
SISSA Library
.
ICTP library
.
Italian National web catalog (SBN)
.
Trieste University web catalog
.
Udine University web catalog
.
© LIBERO v6.4.1sp220816
Page content
You are here
:
Catalogue Display
Catalogue Display
A Survey of Knot Theory
.
Bookmark this Record
Catalogue Record 43141
.
.
Author info on Wikipedia
.
.
LibraryThing
.
.
Google Books
.
.
Amazon Books
.
Catalogue Information
Catalogue Record 43141
.
Reviews
Catalogue Record 43141
.
British Library
Resolver for RSN-43141
Google Scholar
Resolver for RSN-43141
WorldCat
Resolver for RSN-43141
Catalogo Nazionale SBN
Resolver for RSN-43141
GoogleBooks
Resolver for RSN-43141
ICTP Library
Resolver for RSN-43141
.
Share Link
Jump to link
Catalogue Information
Field name
Details
Dewey Class
514.2
Title
A Survey of Knot Theory ([EBook]) / by Akio Kawauchi.
Author
Kawauchi, Akio
Other name(s)
SpringerLink (Online service)
Publication
Basel : Birkhäuser , 1996.
Physical Details
XXI, 423 pages : online resource.
ISBN
9783034892278
Summary Note
Knot theory is a rapidly developing field of research with many applications not only for mathematics. The present volume, written by a well-known specialist, gives a complete survey of knot theory from its very beginnings to today's most recent research results. The topics include Alexander polynomials, Jones type polynomials, and Vassiliev invariants. With its appendix containing many useful tables and an extended list of references with over 3,500 entries it is an indispensable book for everyone concerned with knot theory. The book can serve as an introduction to the field for advanced undergraduate and graduate students. Also researchers working in outside areas such as theoretical physics or molecular biology will benefit from this thorough study which is complemented by many exercises and examples.:
Contents note
0 Fundamentals of knot theory -- 0.1 Spaces -- 0.2 Manifolds and submanifolds -- 0.3 Knots and links -- Supplementary notes for Chapter 0 -- 1 Presentations -- 1.1 Regular presentations -- 1.2 Braid presentations -- 1.3 Bridge presentations -- Supplementary notes for Chapter 1 -- 2 Standard examples -- 2.1 Two-bridge links -- 2.2 Torus links -- 2.3 Pretzel links -- Supplementary notes for Chapter 2 -- 3 Compositions and decompositions -- 3.1 Compositions of links -- 3.2 Decompositions of links -- 3.3 Definition of a tangle and examples -- 3.4 How to judge the non-splittability of a link -- 3.5 How to judge the primeness of a link -- 3.6 How to judge the hyperbolicity of a link -- 3.7 Non-triviality of a link -- 3.8 Conway mutation -- Supplementary notes for Chapter 3 -- 4 Seifert surfaces I: a topological approach -- 4.1 Definition and existence of Seifert surfaces -- 4.2 The Murasugi sum -- 4.3 Sutured manifolds -- Supplementary notes for Chapter 4 -- 5 Seifert surfaces II: an algebraic approach -- 5.1 The Seifert matrix -- 5.2 S-equivalence -- 5.3 Number-theoretic invariants -- 5.4 The reduced link module -- 5.5 The homology of a branched cyclic covering manifold -- Supplementary notes for Chapter 5 -- 6 The fundamental group -- 6.1 Link groups and link group systems -- 6.2 Presentations of a link group -- 6.3 Subgroups and quotient groups of a link group -- Supplementary notes for Chapter 6 -- 7 Multi-variable Alexander polynomials -- 7.1 The Alexander module -- 7.2 Invariants of a A-module -- 7.3 Graded Alexander polynomials -- 7.4 Torres conditions -- Supplementary notes for Chapter 7 -- 8 Jones type polynomials I: a topological approach -- 8.1 The Jones polynomial -- 8.2 The skein polynomial -- 8.3 The Q and Kauffman polynomials -- 8.4 Properties of the polynomial invariants -- 8.5 The skein polynomial via a state model -- Supplementary notes for Chapter 8 -- 9 Jones type polynomials II: an algebraic approach -- 9.1 Preliminaries from representation theory -- 9.2 Link invariants of trace type -- 9.3 The skein polynomial as a link invariant of trace type -- 9.4 The Temperley-Lieb algebra -- Supplementary notes for Chapter 9 -- 10 Symmetries -- 10.1 Periodic knots -- 10.2 Freely periodic knots -- 10.3 Invertible knots -- 10.4 Amphicheiral knots -- 10.5 Symmetries of a hyperbolic knot -- 10.6 The symmetry group -- 10.7 Canonical decompositions and symmetry -- Supplementary notes for Chapter 10 -- 11 Local transformations -- 11.1 Unknotting operations -- 11.2 Properties of X-Gordian distance -- 11.3 Properties of ?-Gordian distance -- 11.4 Properties of #-Gordian distance -- 11.5 Estimation of the X-unknotting number -- 11.6 Local transformations of links -- Supplementary notes for Chapter 11 -- 12 Cobordisms -- 12.1 The knot cobordism group -- 12.2 The matrix cobordism group -- 12.3 Link cobordism -- Supplementary notes for Chapter 12 -- 13 Two-knots I: a topological approach -- 13.1 A normal form -- 13.2 Constructing 2-knots -- 13.3 Seifert hypersurfaces -- 13.4 Exteriors of 2-knots -- 13.5 Cyclic covering spaces -- 13.6 The k-invariant -- 13.7 Ribbon presentations -- Supplementary notes for Chapter 13 -- 14 Two-knots II: an algebraic approach -- 14.1 High-dimensional knot groups -- 14.2 Ribbon 2-knot groups -- 14.3 Torsion elements and the deficiency of 2-knot groups -- Supplementary notes for Chapter 14 -- 15 Knot theory of spatial graphs -- 15.1 Topology of molecules -- 15.2 Uses of the notion of equivalence -- 15.3 Uses of the notion of neighborhood-equivalence -- Supplementary notes for Chapter 15 -- 16 Vassiliev-Gusarov invariants -- 16.1 Vassiliev-Gusarov algebra -- 16.2 Vassiliev-Gusarov invariants and Jones type polynomials -- 16.3 Kontsevich’s iterated integral invariant -- 16.4 Numerical invariants not of Vassiliev-Gusarov type -- Supplementary notes for Chapter 16 -- Appendix A The equivalence of several notions of “link equivalence” -- Appendix B Covering spaces -- Appendix C Canonical decompositions of 3-manifolds -- Appendix D Heegaard splittings and Dehn surgery descriptions -- Appendix E The Blanchfield duality theorem -- Appendix F Tables of data -- References.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-3-0348-9227-8
Links to Related Works
Subject References:
Algebraic Topology
.
Geometry
.
Knot theory
.
Mathematics
.
Authors:
Kawauchi, Akio
.
Corporate Authors:
SpringerLink (Online service)
.
Classification:
514.2
.
514.2 (DDC 22)
.
.
ISBD Display
Catalogue Record 43141
.
Tag Display
Catalogue Record 43141
.
Related Works
Catalogue Record 43141
.
Marc XML
Catalogue Record 43141
.
Add Title to Basket
Catalogue Record 43141
.
Catalogue Information 43141
Beginning of record
.
Catalogue Information 43141
Top of page
.
Download Title
Catalogue Record 43141
Export
This Record
As
Labelled Format
Bibliographic Format
ISBD Format
MARC Format
MARC Binary Format
MARCXML Format
User-Defined Format:
Title
Author
Series
Publication Details
Subject
To
File
Email
Reviews
This item has not been rated.
Add a Review and/or Rating
43141
1
43141
-
2
43141
-
3
43141
-
4
43141
-
5
43141
-
Quick Search
Search for