Last updated November 25, 1998
The 7th Japan-Korea School of Knots and Links
February 15 - 19, 1999
Professor Tsuyoshi Kobayashi will give a lecture at the school
as follows:
Title: Classification of unknotting tunnels for two bridge knots
Abstract: In [R-S1], Rubinstein-Scharlemann introduced a
powerful machinery , what is called {\it graphic}, for studying
Heegaard splittings of 3-manifolds, and obtained deep
results on Reidemeister-Singer distance of two strongly
irreducible Heegaard splittings of a 3-manifold.
In this talk, we introduce an orbifold version of the graphic,
and use it to show that any unknottings tunnel of two bridge
knots are isotopic to known ones. This result together with
Morimoto-Sakuma's [M-S] result gives the complete classification
of unknotting tunnels of two bridge knots.
[R-S1] H. Rubinstein and M. Scharlemann,
Comparing Heegaard splittings of non-Haken 3-manifolds,
Topology 35(1996), 1005--1026.
[M-S] K. Morimoto, and M. Sakuma,
On unknotting tunnels for knots, Math. Ann. 289(1991), 143--167.
Information:
For more information, please send an e-mail to
nakanisi@math.kobe-u.ac.jp