Linking numbers and the Conway polynomial of virtual links.
Saturday, Dec.5, 3:45--4:10


Theorems of Hosokawa, Hartley, and Hoste state that the first non-trivial 
coefficient of the Conway polynomial is equal to a determinant of a 
certain matrix composed of the linking numbers between the components of 
the link. This determinant can be computed using the matrix-tree theorem 
from graph theory. 
   For virtual links there are two different types of the linking number 
and two Conway polynomials, ascending and descending. We generalize the 
theorem above to virtual links. In this case the determinant is related to 
the oriented version of the matrix-tree theorem. This is a joint work with 
my students Z.Cheng, T.Dokos, and J.Lindquist.