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Knots, Links, Spatial Graphs, and Algebraic Invariants
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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
2017.
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| Colección: | Contemporary Mathematics.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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 ₂ᵢ( ).; 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 ℱ( ₆) and ℱ( 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 _{3²,1ⁿ} 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