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Knots, Low-Dimensional Topology and Applications

Knots in Hellas, International Olympic Academy, Greece, July 2016

  • Conference proceedings
  • © 2019

Overview

Editors:
  1. Colin C. Adams

    1. Department of Mathematics, Williams College, Williamstown, USA

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  2. Cameron McA. Gordon

    1. Department of Mathematics, University of Texas at Austin, Austin, USA

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  3. Vaughan F.R. Jones

    1. Department of Mathematics, Vanderbilt University, Nashville, USA

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  4. Louis H. Kauffman

    1. Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, USA

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  5. Sofia Lambropoulou

    1. School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Athens, Greece

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  6. Kenneth C. Millett

    1. Department of Mathematics, University of California, Santa Barbara, Santa Barbara, USA

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  7. Jozef H. Przytycki

    1. Department of Mathematics, Columbian College of Arts & Sciences, George Washington University, Washington, USA

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  8. Renzo Ricca

    1. Department of Mathematics and Applications, University of Milano-Bicocca, Milano, Italy

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  9. Radmila Sazdanovic

    1. Department of Mathematics, North Carolina State University, Raleigh, USA

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  • Collection of high-quality, state-of-the-art research and survey articles
  • Top researchers, including Fields Medal winner like Vaughan Jones
  • Research in new directions, new tools and methods

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 284)

Included in the following conference series:

Conference proceedings info: KNOTS16 2016.

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Table of contents (22 papers)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. A Survey of Hyperbolic Knot Theory

    • David Futer, Efstratia Kalfagianni, Jessica S. Purcell
    Pages 1-30

  3. Spanning Surfaces for Hyperbolic Knots in the 3-Sphere

    • Colin C. Adams
    Pages 31-42

  4. On the Construction of Knots and Links from Thompson’s Groups

    • Vaughan F. R. Jones
    Pages 43-66

  5. Virtual Knot Theory and Virtual Knot Cobordism

    • Louis H. Kauffman
    Pages 67-114

  6. Knot Theory: From Fox 3-Colorings of Links to Yang–Baxter Homology and Khovanov Homology

    • Józef H. Przytycki
    Pages 115-145

  7. Algebraic and Computational Aspects of Quandle 2-Cocycle Invariant

    • W. Edwin Clark, Masahico Saito
    Pages 147-162

  8. A Survey of Quantum Enhancements

    • Sam Nelson
    Pages 163-178

  9. From Alternating to Quasi-Alternating Links

    • Nafaa Chbili
    Pages 179-189

  10. Hoste’s Conjecture and Roots of the Alexander Polynomial

    • Alexander Stoimenov
    Pages 191-206

  11. A Survey of Grid Diagrams and a Proof of Alexander’s Theorem

    • Nancy C. Scherich
    Pages 207-224

  12. Extending the Classical Skein

    • Louis H. Kauffman, Sofia Lambropoulou
    Pages 225-245

  13. From the Framisation of the Temperley–Lieb Algebra to the Jones Polynomial: An Algebraic Approach

    • Maria Chlouveraki
    Pages 247-276

  14. A Note on \(\mathfrak {gl}_{m|n}\) Link Invariants and the HOMFLY–PT Polynomial

    • Hoel Queffelec, Antonio Sartori
    Pages 277-286

  15. On the Geometry of Some Braid Group Representations

    • Mauro Spera
    Pages 287-308

  16. Towards a Version of Markov’s Theorem for Ribbon Torus-Links in \(\mathbb {R}^4\)

    • Celeste Damiani
    Pages 309-328

  17. An Alternative Basis for the Kauffman Bracket Skein Module of the Solid Torus via Braids

    • Ioannis Diamantis
    Pages 329-345

  18. Knot Invariants in Lens Spaces

    • BoÅ¡tjan GabrovÅ¡ek, Eva Horvat
    Pages 347-361

  19. Identity Theorem for Pro-p-groups

    • Andrey M. Mikhovich
    Pages 363-387

  20. A Survey on Knotoids, Braidoids and Their Applications

    • Neslihan Gügümcü, Louis H. Kauffman, Sofia Lambropoulou
    Pages 389-409
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  1. Knots, Low-Dimensional Topology and Applications

Keywords

About this book

This proceedings volume presents a diverse collection of high-quality, state-of-the-art research and survey articles written by top experts in low-dimensional topology and its applications. 

The focal topics include the wide range of historical and contemporary invariants of knots and links and related topics such as three- and four-dimensional manifolds, braids, virtual knot theory, quantum invariants, braids, skein modules and knot algebras, link homology, quandles and their homology; hyperbolic knots and geometric structures of three-dimensional manifolds; the mechanism of topological surgery in physical processes, knots in Nature in the sense of physical knots with applications to polymers, DNA enzyme mechanisms, and protein structure and function. 

The contents is based on contributions presented at the International Conference on Knots, Low-Dimensional Topology and Applications – Knots in Hellas 2016, which was held at the International Olympic Academy in Greece in July 2016. The goal of the international conference was to promote the exchange of methods and ideas across disciplines and generations, from graduate students to senior researchers, and to explore fundamental research problems in the broad fields of knot theory and low-dimensional topology. 

This book will benefit all researchers who wish to take their research in new directions, to learn about new tools and methods, and to discover relevant and recent literature for future study.




Editors and Affiliations

  • Department of Mathematics, Williams College, Williamstown, USA

    Colin C. Adams

  • Department of Mathematics, University of Texas at Austin, Austin, USA

    Cameron McA. Gordon

  • Department of Mathematics, Vanderbilt University, Nashville, USA

    Vaughan F.R. Jones

  • Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, USA

    Louis H. Kauffman

  • School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Athens, Greece

    Sofia Lambropoulou

  • Department of Mathematics, University of California, Santa Barbara, Santa Barbara, USA

    Kenneth C. Millett

  • Department of Mathematics, Columbian College of Arts & Sciences, George Washington University, Washington, USA

    Jozef H. Przytycki

  • Department of Mathematics and Applications, University of Milano-Bicocca, Milano, Italy

    Renzo Ricca

  • Department of Mathematics, North Carolina State University, Raleigh, USA

    Radmila Sazdanovic

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