6 citations · 10 across the 8 of their papers we have counts for
8 papers
Boundary slopes and the numbers of positive/negative crossings for Montesinos knots
Kazuhiro Ichihara, Shigeru Mizushima
We show that a finite numerical boundary slope of an essential surface in the exterior of a Montesinos knot is bounded above and below in terms of the numbers of positive/negative…
Lower bounds on boundary slope diameters for Montesinos knots
Kazuhiro Ichihara, Shigeru Mizushima
In this paper, two lower bounds on the diameters of the boundary slope sets are given for Montesinos knots. One is described in terms of the minimal crossing numbers of the knots,…
Crosscap numbers of pretzel knots
Kazuhiro Ichihara, Shigeru Mizushima
The crosscap number of a knot in the 3-sphere is defined as the minimal first Betti number of non-orientable subsurfaces bounded by the knot. In this paper, we determine the crossc…
Crossing number and diameter of boundary slope set of Montesinos knot
Kazuhiro Ichihara, Shigeru Mizushima
It is shown that the diameter of the boundary slope set is bounded from above by the twice of the minimal crossing number for a Montesinos knot.
Bounds on numerical boundary slopes for Montesinos knots
Kazuhiro Ichihara, Shigeru Mizushima
We give (1) an upper bound on the denominators of numerical boundary slopes and (2) an upper bound on the differences between two numerical boundary slopes, for Montesinos knot ext…
Circle packings on surfaces with projective structures and uniformization
Sadayoshi Kojima, Shigeru Mizushima, Ser Peow Tan
Let Σ_g be a closed orientable surface of genus g \geq 2 and τa graph on Σ_g with one vertex which lifts to a triangulation of the universal cover. We have shown that the cross rat…