arXiv subjects

Seungsang Oh

Publications and source records attributed to Seungsang Oh.

40 records · Page 3Linked to original sources

arXiv2014

Equilateral stick number of knots

An equilateral stick number $s_{=}(K)$ of a knot $K$ is defined to be the minimal number of sticks required to construct a polygonal knot of $K$ which consists of equal length sticks. Rawdon and Scharein [12] found upper bounds for the equilateral stick numbers of all prime knots through 10 crossings by using algorithms in the software KnotPlot. In this paper, we find an upper bound on the equilateral stick number of a nontrivial knot K in terms of the minimal crossing number $c(K)$ which is $s_{=}(K) \le 2c(K) + 2$. Moreover if $K$ is a non-alternating prime knot, then $s_{=}(K) \le 2c(K) - 2$. Furthermore we find another upper bound on the equilateral stick number for composite knots which is $s_{=}(K_1 \# K_2) \le 2c(K_1) + 2c(K_2)$.

math.GT↗

arXiv2003

Reducing Dehn fillings and small surfaces

In this paper we investigate the distances between Dehn fillings on a hyperbolic 3-manifold that yield 3-manifolds containing essential small surfaces including non-orientable surfaces. Especially we study the situations where one filling creates an essential sphere or projective plane, and the other creates an essential sphere, projective plane, annulus, Moebius band, torus or Klein bottle,all 11 pairs of such non-hyperbolic manifolds.

math.GT↗

arXiv2000

Dehn fillings creating essential spheres and tori

Let $M$ be a simple 3-manifold with a toral boundary component. It is known that if two Dehn fillings on $M$ along the boundary produce a reducible manifold and a toroidal manifold, then the distance between the filling slopes is at most three. This paper gives a remarkably short proof of this result.

math.GT↗

arXiv2000

P^2-reducing and toroidal Dehn fillings

We study the situation where we have two exceptional Dehn fillings on a given hyperbolic 3-manifold. We consider two cases that one filling creates a projective plane, and the other creates an essential torus or a Klein bottle, and give the best possible upper bound on the distance between two fillings for each case.

math.GT↗