Mutant knots and intersection graphs

Chmutov, Sergei; Lando, Sergei

doi:10.2140/agt.2007.7.1579

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Mutant knots and intersection graphs

Sergei V Chmutov and Sergei K Lando

Algebraic & Geometric Topology 7 (2007) 1579–1598

DOI: 10.2140/agt.2007.7.1579

arXiv: math.GT/0704.1313

Abstract

We prove that if a finite order knot invariant does not distinguish mutant knots, then the corresponding weight system depends on the intersection graph of a chord diagram rather than on the diagram itself. Conversely, if we have a weight system depending only on the intersection graphs of chord diagrams, then the composition of such a weight system with the Kontsevich invariant determines a knot invariant that does not distinguish mutant knots. Thus, an equivalence between finite order invariants not distinguishing mutants and weight systems depending only on intersections graphs is established. We discuss the relationship between our results and certain Lie algebra weight systems.

Keywords

mutant knots, Vassiliev invariants, intersection graphs, Lie algebra weight systems

Mathematical Subject Classification 2000

Primary: 57M25, 57M15

Secondary: 57M27, 05C10

References

Publication

Received: 16 May 2007

Revised: 14 September 2007

Accepted: 17 September 2007

Published: 17 December 2007

Authors

Sergei V Chmutov
The Ohio State University - Mansfield 1680 University Drive Mansfield OH 44906 USA
http://www.math.ohio-state.edu/~chmutov/
Sergei K Lando
Institute for System Research RAS and the Poncelet Laboratory Independent University of Moscow Bolshoy Vlasyevskiy Pereulok 11 Moscow 119002 Russia
http://www.mccme.ru/ium/~lando/

Volume 7, issue 3 (2007)