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The Resource Knots, Links, Spatial Graphs, and Algebraic Invariants

Knots, Links, Spatial Graphs, and Algebraic Invariants

Label
Knots, Links, Spatial Graphs, and Algebraic Invariants
Title
Knots, Links, Spatial Graphs, and Algebraic Invariants
Creator
Contributor
Subject
Genre
Language
eng
Summary
This volume contains the proceedings of the AMS Special Session on Algebraic and Combinatorial Structures in Knot Theory and the AMS Special Session on Spatial Graphs, both held from October 24-25, 2015, at California State University, Fullerton, CA. Included in this volume are articles that draw on techniques from geometry and algebra to address topological problems about knot theory and spatial graph theory, and their combinatorial generalizations to equivalence classes of diagrams that are preserved under a set of Reidemeister-type moves. The interconnections of these areas and their connec
Member of
Cataloging source
EBLCP
http://library.link/vocab/creatorName
Flapan, Erica
Dewey number
514.2242
Index
no index present
LC call number
QA612.2.K565 2017
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
  • Henrich, Allison
  • Kaestner, Aaron
  • Nelson, Sam
Series statement
Contemporary Mathematics
Series volume
v.689
http://library.link/vocab/subjectName
  • Knot theory
  • Link theory
  • Graph theory
  • Invariants
  • Manifolds and cell complexes -- Low-dimensional topology -- Relations with graph theory
  • Graph theory
  • Invariants
  • Knot theory
  • Link theory
Label
Knots, Links, Spatial Graphs, and Algebraic Invariants
Instantiates
Publication
Note
  • Description based upon print version of record
  • Partially multiplicative biquandles and handlebody-knots
Contents
  • Cover; Title page; Contents; Preface: Knots, graphs, algebra & combinatorics; Part I: Knot Theoretic Structures; Part II: Spatial Graph Theory; References; The first coefficient of Homflypt and Kauffman polynomials: Vertigan proof of polynomial complexity using dynamic programming; 1. Introduction; 2. Computation of 0( ); 3. Computation of 2{u1D62}( ).; 4. Coefficients of the Kauffman polynomial, _{ }( , ).; 5. Polynomials of virtual diagrams.; 6. Dynamic programming; 7. Knotoids of Vladimir Turaev; 8. Acknowledgements; References
  • Linear Alexander quandle colorings and the minimum number of colors1. Introduction; 2. Review of Quandles; 3. Coloring of Knots by Linear Alexander Quandles of order 5; 4. Main Result; 5. Four Colors is the Minimum Number of Colors; References; Quandle identities and homology; 1. Introduction; 2. Preliminary; 3. Type 3 quandles; 4. From identities to extensions and subcomplexes; 5. Inner identities; Acknowledgements; References; Ribbonlength of folded ribbon unknots in the plane; 1. Introduction; 2. Modeling Folded Ribbon Knots; 3. Ribbon Equivalence; 4. Ribbonlength
  • 5. Local structure of folded ribbon knots6. Projection stick index and ribbonlength; Acknowledgments; References; Checkerboard framings and states of virtual link diagrams; 1. Introduction; 2. Virtual knots; 3. The Bracket polynomial; 4. Establishing the result; 5. Conclusion; References; Virtual covers of links II; 1. Background; 2. Semi-Fibered Concordance; 3. Ribbon and Slice Obstructions; 4. Injectivity of Satellite Operators; 5. Concordance and Cables of Knots in 3-manifolds; Acknowledgments; References; Recent developments in spatial graph theory; 1. Introduction
  • 2. Intrinsic linking and knotting3. -apex graphs; 4. Conway-Gordon type theorems for graphs in {u2131}( 6) and {u2131}( 7); 5. Conway-Gordon type theorems for _{3,3,1,1}; 6. Linear embeddings of graphs; 7. Symmetries of spatial graphs in 3; 8. Graphs embedded in 3-Manifolds; References; Order nine MMIK graphs; Introduction; 1. Definitions and Lemmas; 2. Proof of Proposition 2; 3. Proof of Proposition 4; 4. Computer Verification for Size 23 through 27; Acknowledgements; References; A chord graph constructed from a ribbon surface-link; 1. Introduction
  • 2. How to transform a (welded virtual) link diagram into a chord diagram without base crossing3. How to transform a chord graph into a ribbon surface-link in 4-space; 4. How to modify the moves on a chord diagram into the moves on a chord diagram without base crossing; References; The _{ +5} and _{32,1{u207F}} families and obstructions to -apex.; Introduction; 1. Proof of Theorem 3; 2. Results for \On{2} and \On{3}; Appendix A. Edge lists of 8 family graphs; Appendix B. 8 family graphs are not 3-apex; Appendix C. Proper minors are 3-apex; References
Control code
993763011
Dimensions
unknown
Extent
1 online resource (202 p.)
Form of item
online
Isbn
9781470440770
Specific material designation
remote
System control number
(OCoLC)993763011
Label
Knots, Links, Spatial Graphs, and Algebraic Invariants
Publication
Note
  • Description based upon print version of record
  • Partially multiplicative biquandles and handlebody-knots
Contents
  • Cover; Title page; Contents; Preface: Knots, graphs, algebra & combinatorics; Part I: Knot Theoretic Structures; Part II: Spatial Graph Theory; References; The first coefficient of Homflypt and Kauffman polynomials: Vertigan proof of polynomial complexity using dynamic programming; 1. Introduction; 2. Computation of 0( ); 3. Computation of 2{u1D62}( ).; 4. Coefficients of the Kauffman polynomial, _{ }( , ).; 5. Polynomials of virtual diagrams.; 6. Dynamic programming; 7. Knotoids of Vladimir Turaev; 8. Acknowledgements; References
  • Linear Alexander quandle colorings and the minimum number of colors1. Introduction; 2. Review of Quandles; 3. Coloring of Knots by Linear Alexander Quandles of order 5; 4. Main Result; 5. Four Colors is the Minimum Number of Colors; References; Quandle identities and homology; 1. Introduction; 2. Preliminary; 3. Type 3 quandles; 4. From identities to extensions and subcomplexes; 5. Inner identities; Acknowledgements; References; Ribbonlength of folded ribbon unknots in the plane; 1. Introduction; 2. Modeling Folded Ribbon Knots; 3. Ribbon Equivalence; 4. Ribbonlength
  • 5. Local structure of folded ribbon knots6. Projection stick index and ribbonlength; Acknowledgments; References; Checkerboard framings and states of virtual link diagrams; 1. Introduction; 2. Virtual knots; 3. The Bracket polynomial; 4. Establishing the result; 5. Conclusion; References; Virtual covers of links II; 1. Background; 2. Semi-Fibered Concordance; 3. Ribbon and Slice Obstructions; 4. Injectivity of Satellite Operators; 5. Concordance and Cables of Knots in 3-manifolds; Acknowledgments; References; Recent developments in spatial graph theory; 1. Introduction
  • 2. Intrinsic linking and knotting3. -apex graphs; 4. Conway-Gordon type theorems for graphs in {u2131}( 6) and {u2131}( 7); 5. Conway-Gordon type theorems for _{3,3,1,1}; 6. Linear embeddings of graphs; 7. Symmetries of spatial graphs in 3; 8. Graphs embedded in 3-Manifolds; References; Order nine MMIK graphs; Introduction; 1. Definitions and Lemmas; 2. Proof of Proposition 2; 3. Proof of Proposition 4; 4. Computer Verification for Size 23 through 27; Acknowledgements; References; A chord graph constructed from a ribbon surface-link; 1. Introduction
  • 2. How to transform a (welded virtual) link diagram into a chord diagram without base crossing3. How to transform a chord graph into a ribbon surface-link in 4-space; 4. How to modify the moves on a chord diagram into the moves on a chord diagram without base crossing; References; The _{ +5} and _{32,1{u207F}} families and obstructions to -apex.; Introduction; 1. Proof of Theorem 3; 2. Results for \On{2} and \On{3}; Appendix A. Edge lists of 8 family graphs; Appendix B. 8 family graphs are not 3-apex; Appendix C. Proper minors are 3-apex; References
Control code
993763011
Dimensions
unknown
Extent
1 online resource (202 p.)
Form of item
online
Isbn
9781470440770
Specific material designation
remote
System control number
(OCoLC)993763011

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