Thursday, May 19, 2011. 14:15-15:15.

Title: Combinatorics of virtual links.

Abstract.
Virtual links, introduced by L.Kauffman and independently by M.Polyak and O.Viro, 
are represented by diagrams similar to ordinary knot diagrams, except some 
crossings are designated as virtual. They are similar to extra crossings 
on planar pictures of non planar graphs. Topologically they can be regarded as 
links in thickened surfaces when the equivalence involve not only usual isotopy 
but also a surgery of the surface. Comparably with ordinary links in 3-space they 
are more close to combinatorics. Recently it was observed by H.Dye and L.Kauffman, 
and by Y.Miyazawa that for virtual links the Jones polynomial can be split into 
several parts which are invariant individually. These additional parts do not 
arise in the case of classical links. The generating function of these parts was 
called arrow polynomial.
    In the talk I briefly review virtual link theory, introduce the arrow 
polynomial, and explain an arrow generalization of the Thistlethwaite theorem 
expressing the Jones polynomial as a specialization of the Tutte polynomial.