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The Mathematics of Knots

Theory and Application

  • Book
  • © 2011

Overview

Editors:
  1. Markus Banagl

    1. Department of Mathematics, University of Heidelberg, Heidelberg, Germany

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    You can also search for this editor in PubMed   Google Scholar

  2. Denis Vogel

    1. Department of Mathematics, University of Heidelberg, Heidelberg, Germany

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    You can also search for this editor in PubMed   Google Scholar

  • Brings the reader up to date on the currently most actively pursued areas of mathematical knot theory
  • Contains applications to cell biology and mathematical physics, contains survey papers as well as original research results
  • Treats low dimensional knots as well as high dimensional knots
  • Includes supplementary material: sn.pub/extras

Part of the book series: Contributions in Mathematical and Computational Sciences (CMCS, volume 1)

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-X
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  2. Knots, Singular Embeddings, and Monodromy

    • Markus Banagl, Sylvain E. Cappell, Julius L. Shaneson
    Pages 1-30

  3. Lower Bounds on Virtual Crossing Number and Minimal Surface Genus

    • Kumud Bhandari, H. A. Dye, Louis H. Kauffman
    Pages 31-43

  4. A Survey of Twisted Alexander Polynomials

    • Stefan Friedl, Stefano Vidussi
    Pages 45-94

  5. On Two Categorifications of the Arrow Polynomial for Virtual Knots

    • Heather Ann Dye, Louis Hirsch Kauffman, Vassily Olegovich Manturov
    Pages 95-124

  6. An Adelic Extension of the Jones Polynomial

    • Jesús Juyumaya, Sofia Lambropoulou
    Pages 125-142

  7. Legendrian Grid Number One Knots and Augmentations of Their Differential Algebras

    • Joan E. Licata
    Pages 143-168

  8. Embeddings of Four-valent Framed Graphs into 2-surfaces

    • Vassily Olegovich Manturov
    Pages 169-197

  9. Geometric Topology and Field Theory on 3-Manifolds

    • Kishore Marathe
    Pages 199-256

  10. From Goeritz Matrices to Quasi-alternating Links

    • Józef H. Przytycki
    Pages 257-316

  11. An Overview of Property 2R

    • Martin Scharlemann
    Pages 317-325

  12. DNA, Knots and Tangles

    • De Witt Sumners
    Pages 327-353

  13. Back Matter

    Pages 355-357
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Keywords

About this book

The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursued areas of mathematical knot theory and its applications in mathematical physics and cell biology. Both original research and survey articles are presented; numerous illustrations support the text. The book will be of great interest to researchers in topology, geometry, and mathematical physics, graduate students specializing in knot theory, and cell biologists interested in the topology of DNA strands.

Editors and Affiliations

  • Department of Mathematics, University of Heidelberg, Heidelberg, Germany

    Markus Banagl, Denis Vogel

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