Bypasses for rectangular diagrams. Proof of Jones' conjecture and related questions
Geometric Topology
2013-10-22 v2
Abstract
In the present paper a criteria for a rectangular diagram to admit a simplification is given in terms of Legendrian knots. It is shown that there are two types of simplifications which are mutually independent in a sense. A new proof of the monotonic simplification theorem for the unknot is given. It is shown that a minimal rectangular diagram maximizes the Thurston--Bennequin number for the corresponding Legendrian links. Jones' conjecture about the invariance of the algebraic number of intersections of a minimal braid representing a fixed link type is proved.
Keywords
Cite
@article{arxiv.1206.0898,
title = {Bypasses for rectangular diagrams. Proof of Jones' conjecture and related questions},
author = {Ivan Dynnikov and Maxim Prasolov},
journal= {arXiv preprint arXiv:1206.0898},
year = {2013}
}
Comments
50 pages, 62 Figures, numerous minor corrections