The Resource Diagram genus, generators, and applications, Alexander Stoimenow, GIST College, Gwangju Institute of Science and Technology Gwangju, South Korea

Diagram genus, generators, and applications, Alexander Stoimenow, GIST College, Gwangju Institute of Science and Technology Gwangju, South Korea

Label
Diagram genus, generators, and applications
Title
Diagram genus, generators, and applications
Statement of responsibility
Alexander Stoimenow, GIST College, Gwangju Institute of Science and Technology Gwangju, South Korea
Creator
Contributor
Author
Provider
Subject
Language
eng
Member of
Cataloging source
NhCcYBP
http://library.link/vocab/creatorName
Stoimenow, Alexander
Illustrations
illustrations
Index
no index present
LC call number
QA612.2
LC item number
.S76 2016
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorName
ebrary
Series statement
Monographs and research notes in mathematics
http://library.link/vocab/subjectName
  • Knot theory
  • Knot polynomials
Label
Diagram genus, generators, and applications, Alexander Stoimenow, GIST College, Gwangju Institute of Science and Technology Gwangju, South Korea
Instantiates
Publication
Copyright
Note
"A Chapman & Hall Book."
Bibliography note
Includes bibliographical references (pages 159-166)
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Machine generated contents note: 1.Introduction -- 1.1.The beginning of knot theory -- 1.2.Reidemeister moves and invariants -- 1.3.Combinatorial knot theory -- 1.4.Genera of knots -- 1.5.Overview of results -- 1.5.1.General generator estimates -- 1.5.2.Compilation of knot generators of genus 4 -- 1.5.3.Unknot diagrams -- 1.5.4.Non-triviality of the link polynomials -- 1.5.5.Signature of positive knots -- 1.5.6.Braid index and Bennequin surfaces -- 1.5.7.Properties of the Alexander polynomial of alternating knots -- 1.6.Issues of presentation -- 1.7.Further applications -- 2.Preliminaries -- 2.1.Knots and diagrams -- 2.2.Crossing number and writhe -- 2.3.Knotation and not-tables -- 2.4.Seifert surfaces and genera -- 2.4.1.Special diagrams -- 2.5.Graphs -- 2.5.1.General definitions -- 2.5.2.The checkerboard coloring and checkerboard graph -- 2.6.Diagrammatic moves -- 2.6.1.Flypes and mutations -- 2.6.2.Bridges and wave moves -- 2.7.Braids and braid representations -- 2.8.Link polynomials -- 2.8.1.Generalities -- 2.8.2.Skein, Jones, and Alexander polynomial -- 2.8.3.Kauffman polynomial and semiadequacy -- 2.9.MWF inequality, Seifert graph and graph index -- 2.10.The signature -- 2.11.Genus generators -- 2.12.Knots vs. links -- 3.The maximal number of generator crossings and ~ -equivalence classes -- 3.1.Generator crossing number inequalities -- 3.2.An algorithm for special diagrams -- 3.3.Proof of the inequalities -- 3.4.Applications and improvements -- 4.Generators of genus 4 -- 5.Unknot diagrams, non-trivial polynomials and achiral knots -- 5.1.Some preparations and special cases -- 5.2.Reduction of unknot diagrams -- 5.3.Simplifications -- 5.4.Examples -- 5.5.Non-triviality of skein and Jones polynomial -- 5.6.On the number of unknotting Reidemeister moves -- 5.7.Achiral knot classification -- 6.The signature -- 7.Braid index of alternating knots -- 7.1.Motivation and history -- 7.2.Hidden Seifert circle problem -- 7.3.Modifying the index -- 7.4.Simplified regularization -- 7.5.A conjecture -- 8.Minimal string Bennequin surfaces -- 8.1.Statement of result -- 8.2.The restricted index -- 8.3.Finding a minimal string Bennequin surface -- 9.The Alexander polynomial of alternating knots -- 9.1.Hoste's conjecture -- 9.2.The log-concavity conjecture -- 9.3.Complete linear relations by degree -- 9.3.1.Linear relations up to constants -- 9.3.2.General genus -- 9.3.3.Removing inaccuracy up to constants -- 10.Outlook -- 10.1.Legendrian invariants and braid index -- 10.2.Minimal genus and fibering of canonical surfaces -- 10.3.Wicks forms, markings, enumeration of alternating knots by genus -- 10.4.Crossing numbers -- 10.5.Canonical genus bounds hyperbolic volume -- 10.6.The relation between volume and the sln polynomial -- 10.7.Everywhere equivalent links
Extent
1 online resource ( xviii, 169 pages)
Form of item
online
Isbn
9781498733823
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations.
Reproduction note
Electronic reproduction.
Stock number
99968388862
System control number
(NhCcYBP)12590574
Label
Diagram genus, generators, and applications, Alexander Stoimenow, GIST College, Gwangju Institute of Science and Technology Gwangju, South Korea
Publication
Copyright
Note
"A Chapman & Hall Book."
Bibliography note
Includes bibliographical references (pages 159-166)
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Machine generated contents note: 1.Introduction -- 1.1.The beginning of knot theory -- 1.2.Reidemeister moves and invariants -- 1.3.Combinatorial knot theory -- 1.4.Genera of knots -- 1.5.Overview of results -- 1.5.1.General generator estimates -- 1.5.2.Compilation of knot generators of genus 4 -- 1.5.3.Unknot diagrams -- 1.5.4.Non-triviality of the link polynomials -- 1.5.5.Signature of positive knots -- 1.5.6.Braid index and Bennequin surfaces -- 1.5.7.Properties of the Alexander polynomial of alternating knots -- 1.6.Issues of presentation -- 1.7.Further applications -- 2.Preliminaries -- 2.1.Knots and diagrams -- 2.2.Crossing number and writhe -- 2.3.Knotation and not-tables -- 2.4.Seifert surfaces and genera -- 2.4.1.Special diagrams -- 2.5.Graphs -- 2.5.1.General definitions -- 2.5.2.The checkerboard coloring and checkerboard graph -- 2.6.Diagrammatic moves -- 2.6.1.Flypes and mutations -- 2.6.2.Bridges and wave moves -- 2.7.Braids and braid representations -- 2.8.Link polynomials -- 2.8.1.Generalities -- 2.8.2.Skein, Jones, and Alexander polynomial -- 2.8.3.Kauffman polynomial and semiadequacy -- 2.9.MWF inequality, Seifert graph and graph index -- 2.10.The signature -- 2.11.Genus generators -- 2.12.Knots vs. links -- 3.The maximal number of generator crossings and ~ -equivalence classes -- 3.1.Generator crossing number inequalities -- 3.2.An algorithm for special diagrams -- 3.3.Proof of the inequalities -- 3.4.Applications and improvements -- 4.Generators of genus 4 -- 5.Unknot diagrams, non-trivial polynomials and achiral knots -- 5.1.Some preparations and special cases -- 5.2.Reduction of unknot diagrams -- 5.3.Simplifications -- 5.4.Examples -- 5.5.Non-triviality of skein and Jones polynomial -- 5.6.On the number of unknotting Reidemeister moves -- 5.7.Achiral knot classification -- 6.The signature -- 7.Braid index of alternating knots -- 7.1.Motivation and history -- 7.2.Hidden Seifert circle problem -- 7.3.Modifying the index -- 7.4.Simplified regularization -- 7.5.A conjecture -- 8.Minimal string Bennequin surfaces -- 8.1.Statement of result -- 8.2.The restricted index -- 8.3.Finding a minimal string Bennequin surface -- 9.The Alexander polynomial of alternating knots -- 9.1.Hoste's conjecture -- 9.2.The log-concavity conjecture -- 9.3.Complete linear relations by degree -- 9.3.1.Linear relations up to constants -- 9.3.2.General genus -- 9.3.3.Removing inaccuracy up to constants -- 10.Outlook -- 10.1.Legendrian invariants and braid index -- 10.2.Minimal genus and fibering of canonical surfaces -- 10.3.Wicks forms, markings, enumeration of alternating knots by genus -- 10.4.Crossing numbers -- 10.5.Canonical genus bounds hyperbolic volume -- 10.6.The relation between volume and the sln polynomial -- 10.7.Everywhere equivalent links
Extent
1 online resource ( xviii, 169 pages)
Form of item
online
Isbn
9781498733823
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations.
Reproduction note
Electronic reproduction.
Stock number
99968388862
System control number
(NhCcYBP)12590574

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