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Applications to Knot Theory

  • Joanna A. Ellis-Monaghan
  • Iain Moffatt
Chapter
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

In this chapter we give an overview of some recent connections between knot theory and graph theory. After giving a quick overview of classical links, links in thickened surfaces and virtual links, we explain some of the ways in which embedded graphs can be used to describe link diagrams. We go on to describe various recent connections between the ribbon graph polynomial, and the Jones and HOMFLY-PT polynomial of a link. For classical links, these give connections between knot polynomials and the Tutte polynomial.

Keywords

Virtual Link Ribbon Graph Jones Polynomial Reidemeister Move Tutte Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Joanna A. Ellis-Monaghan, Iain Moffatt 2013

Authors and Affiliations

  • Joanna A. Ellis-Monaghan
    • 1
  • Iain Moffatt
    • 2
  1. 1.Department of MathematicsSaint Michael’s CollegeColchesterUSA
  2. 2.Department of MathematicsRoyal Holloway University of LondonEgham, SurreyUK

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