Original Article
Kyungpook Mathematical Journal 2009; 49(2): 321-348
Published online June 23, 2009
Copyright © Kyungpook Mathematical Journal.
Lower Bounds on Boundary Slope Diameters for Montesinos Knots
Kazuhiro Ichihara1, Shigeru Mizushima2
1Department of Mathematics Education, Nara University of Education, Takabatakecho, Nara, 630{8528, Japan
2 Department of Mathematical and Computing Sciences, Tokyo Institute of Technoogy, 2{12{1 Ohokayama, Meguro, Tokyo 152{8552, Japan
In this paper, we give two lower bounds on the diameter of the boundary slope set of a Montesinos knot. One is described in terms of the minimal crossing numbers of the knots, and the other is related to the Euler characteristics of essential surfaces with the maximal/minimal boundary slopes.
Keywords: boundary slopes, diameter, Montesinos knot