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Linking numbers and the Conway polynomial of virtual links
by
Sergei Chmutov
Ohio State University, Mansfield
Coauthors: Z.Cheng, T.Dokos, J.Lindquist
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.
Date received: November 21, 2009
Copyright © 2009 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 # cazp-10.