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Partial-dual genus polynomial as a weight system

Sergei Chmutov

Abstract

We prove that the partial-dual genus polynomial considered as a function on chord diagrams satisfies the four-term relation. Thus it is a weight system from the theory of Vassiliev knot invariants.

Partial-dual genus polynomial as a weight system

Abstract

We prove that the partial-dual genus polynomial considered as a function on chord diagrams satisfies the four-term relation. Thus it is a weight system from the theory of Vassiliev knot invariants.
Paper Structure (10 sections, 21 equations, 1 table)

This paper contains 10 sections, 21 equations, 1 table.

Table of Contents

  1. Introduction
  2. Ribbon graphs
  3. Partial duality.
  4. Partial-dual genus polynomial.
  5. Chord diagrams
  6. Four-term relation for chord diagrams.
  7. Ribbon graphs from chord diagrams.
  8. Partial duality in terms of chord diagrams.
  9. Main result
  10. Open problems

Theorems & Definitions (1)

  • proof