Topology Atlas | Conferences

Knots in Washington XXXI; Categorification, Quandles, Quantum knots and Quantum computing
December 3-5, 2010
George Washington University
Washington, DC, USA

Organizers
Valentina Harizanov (GWU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU, NSF), Radmila Sazdanovic (U.Penn), Alexander Shumakovitch (GWU), Hao Wu (GWU)

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Finite type invariants obtained by counting surfaces
by
Michael Brandenbursky
Department of Mathematics, Vanderbilt University
Coauthors: Michael Polyak

A Gauss diagram is a simple, combinatorial way to present a knot. It is known that any Vassiliev invariant may be obtained from a Gauss diagram formula that involves counting (with signs and multiplicities) subdiagrams of certain combinatorial types. These formulas generalize the calculation of a linking number by counting signs of crossings in a link diagram.

Until recently, explicit formulas of this type were known only for few invariants of low degrees. I will present simple formulas for an infinite family of invariants arising from the HOMFLY-PT polynomial. I will also discuss an interesting interpretation of these formulas in terms of counting surfaces of a certain genus and number of boundary components in a Gauss diagram.

Date received: November 1, 2010

Copyright © 2010 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 # cbbr-07.