Summary: 1
Date
Abstract
Introduction and overview
THERE ARE NO UNEXPECTED TUNNEL NUMBER
ONE KNOTS OF GENUS ONE
MARTIN SCHARLEMANN
. We show that the only knots that are tunnel num-
ber one and genus one are those that are already known: 2-bridge
knots obtained by plumbing together two unknotted annuli and the
satellite examples classied by Eudave-Mu~noz and by Morimoto-
Sakuma. This conrms a conjecture rst made by Goda and Ter-
agaito.
: June 2, 2001.
Research supported in part by an NSF grant, the Miller Institute, and RIMS
Kyoto.
1.
There are many useful ways of indexing the complexity of knot types:
crossing number, bridge number, tunnel number, genus, etc. Often the
relationship between these indices is unclear, and sometimes it is clear

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

Collections: Mathematics