Bypasses for rectangular diagrams. Proof of Jones' conjecture and related questions

Ivan Dynnikov; Maxim Prasolov

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arXiv · 1206.0898

Bypasses for rectangular diagrams. Proof of Jones' conjecture and related questions

Ivan Dynnikov·Maxim Prasolov

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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.

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Ivan Dynnikov, Maxim Prasolov. 2013-03-24. Bypasses for rectangular diagrams. Proof of Jones' conjecture and related questions. https://arxiv.org/abs/1206.0898

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