arXiv subjects

Tsuyoshi Kobayashi

Publications and source records attributed to Tsuyoshi Kobayashi.

21 records · Page 2Linked to original sources

arXiv2002

Local detection of strongly irreducible Heegaard splittings via knot exteriors

We study the way a strongly irreducible Heegaard surface $Σ$ intersects a knot exterior $X$ embedded in a 3-manifold, and show that if $Σ\cap \partial X$ consists of simple closed curves which are essential in both $Σ$ and $\partial X$, then the intersection $X \cap Σ$ consists of meridional annuli only. As an application we show that when considering two Heegaard surfaces that intersect essentially and spinally (cf. Rubinstein and Shcarlemann) any embedded torus in the union of the two bounds a solid torus.

math.GT↗

arXiv2001

Heegaard splittings of exteriors of, two bridge knots

In this paper, we show that, for each non-trivial two bridge knot K and for each g > 2, every genus g Heegaard splitting of the exterior E(K) of K is reducible.

math.GT↗

arXiv1999

Classification of unknotting tunnels for two bridge knots

In this paper, we show that any unknotting tunnel for a two bridge knot is isotopic to either one of known ones. This together with Morimoto-Sakuma's result gives the complete classification of unknotting tunnels for two bridge knots up to isotopies and homeomorphisms.

math.GT↗