Topology Atlas | Conferences

Knots in Washington XXXVII
January 19-20, 2014
George Washington University
Washington, DC, USA

Organizers
Mieczyslaw K. Dabkowski (UT Dallas), Valentina Harizanov (GWU), Jozef H. Przytycki (GWU and UMCP), Yongwu Rong (GWU), Radmila Sazdanovic (NCSU), Alexander Shumakovitch (GWU), Hao Wu (GWU)

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A Geometric Description of Turaev Surfaces
by
Cody Armond
University of Iowa
Coauthors: Nathan Druivenga, Thomas Kindred

Turaev surfaces are surfaces constructed from a knot diagram, which were originally studied to help solve the problem of whether reduced alternating diagrams have minimal crossing number. They are constructed from two opposing state arising in the state sum formula of the Kauffman bracket polynomial. Since then, they have been further studied and have been shown to have relationships with the rank polynomial for ribbon graphs as well as knot Floer homology and Khovanov homology.

We present a description of Turaev surfaces which is not dependent on knot diagrams, and is instead described as a Heegard splitting of S3 with special properties.

Date received: December 15, 2013

Copyright © 2013 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 # cbid-12.