Heidelberg Knot Theory Semester
Mon. Dec. 15 - Fr. Dec. 19, 2008.
http://www.mathi.uni-heidelberg.de/~banagl/hkts.htm


Title: Combinatorics of Gauss diagrams and the HOMFLYPT polynomial.

Abstract:
Many link invariants can be expressed in terms of Gauss diagrams. In
particular any Vassiliev knot invariant can be expressed in
terms of some "subdiagrams" of the Gauss diagram. I'll discuss this
approach to invariants coming from the HOMFLYPT polynomial. This approach
allows to define HOMFLYPT polynomial for links with ordered components and
with a based point on each component. Such definition directly extends to
virtual links. Our description generalizes the Gauss diagram formulas for
the Conway polynomial obtained earlier jointly with Michael Khoury and
Alfred Rossi. This is a joint work with Michael Polyak.