Quantum Topology / Hopf Algebra Seminar
Eiji Ogasa
UIC and Meiji Gakuin University
Local move identities for the Alexander polynomial
Abstract: The Alexander polynomial of 1-links satisfies a very well-known local move identity.
We show that the Alexander polynomial of high dimensional knots satisfies two kinds of local move identities.
One is a new type: (K_+) - (K_-)=(t+1)(K_0). The other is the same one as in the 1-link case.
(K_+) - (K_-)=(t-1)(K_0).
Reference:
Louis H. Kauffman and Eiji Ogasa: Local moves on knots and products of knots
Fund. Math. Volume three of Knots in Poland III Banach Center Publications (to appear), arXiv:1210.4667[math.GT]
Eiji Ogasa: Local move identities for the Alexander polynomials of high-dimensional knots and inertia groups.
J. Knot Theory Ramifications 18 (2009), no. 4, 531-545.
Eiji Ogasa: Ribbon-moves of 2-links preserve the mu-invariant of 2-links.
J. Knot Theory Ramifications 13 (2004), no. 5, 669-687.
Thursday September 11, 2014 at 3:00 PM in SEO 512