Last updated January 12, 1999
The 7th Japan-Korea School of Knots and Links
February 15 - 19, 1999
Professor Taizo Kanenobu will give a lecture at the school
as follows:
Title: Link Polynomials and Finite Type Invariants
Abstract:
In the first half of this lecture,
a definition of a finite type (Vassiliev) invariant
for a knot will be given in an elementary way.
We then show that each of the Conway, Jones, and HOMFLY polynomials
is equivalent to an infinite sequence of finite type invariatns.
We refer:
J. S. Birman: On the combinatorics of Vassiliev invariants,
in Braid group, knot theory and statistical mechanics II,
(M. L. Ge and C. N. Yang, eds.),
Advanced Series in Mathematical Physics,
World Scientific (1994), pp. 1--19.
and
Chapter 15, Vassiliev Invariants
in
K. Murasugi: Knot Theory and its Applications,
Birkhauser, Boston, (1996).
In the latter half, we consider a finite type invariant for
an oriented link. In particular, we focus on linking numbers and give a new
proof for a formula of Hoste concerning the first coefficient of the Conway
polynomial of a link using finite type invariants. Furthermore,
generalizing this formula, we evaluate the coefficient polynomials of the
HOMFLY polynomial of a link,
which also generalizes a formula of Lickorish and Millett.
We refer:
T. Kanenobu, Y. Miyazawa and A. Tani: Vassiliev link invariants of order
three, J. Knot Theory Ramifications 7 (1998), no. 4, 433--462.
T. Kanenobu: An evaluation of the coefficient polynomial of the HOMFLY
polynomial of a link, preprint.
Information:
For more information, please send an e-mail to
nakanisi@math.kobe-u.ac.jp