Topology Atlas | Conferences

Conference on Knot Theory and Its Applications to Physics and Quantum Computing; 60th birthday of Jozef H. Przytycki
January 6-9, 2015
University of Texas at Dallas
Richardson, TX, USA

Organizers
Mieczyslaw K. Dabkowski (UTD) Tobias Hagge (UTD) Valentina S. Harizanov (GWU) Viswanath Ramakrishna (UTD) Radmila Sazdanovic (NCSU) Adam S. Sikora (SUNYUB)

Conference Homepage


Monotonic simplification and contact topology
by
Ivan Dynnikov
Steklov Mathematical Institute
Coauthors: Maxim Prasolov

Rectangular (or grid) diagrams provide for a good formalism for describing ordinary links, closed braids, Legendrian and transverse links. We show that a rectangular diagram admits a simplification by elementary moves if and only if one of the two Legendrian links associated to the diagram admits a destabilization. This has a number of consequences including the generalized Jones conjecture about braids and the existence of an algorithm to determine the maximal Thurston-Bennequin number of a link. This may also have some more consequences for algorithmic classification of links if certain results about Legendrian links are proven.

Date received: December 22, 2014

Copyright © 2014 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbjz-68.