3 citations · 4 across the 4 of their papers we have counts for
5 papers
Heegaard genus of the connected sum of m-small knots
Tsuyoshi Kobayashi, Yo'av Rieck
We prove that if are m-small knots in closed orientable 3-manifolds then the Heegaard genus of $E(#_{i=1}^n K_i)$ is strictly less than the su…
On the growth rate of tunnel number of knots
Tsuyoshi Kobayashi, Yo'av Rieck
Given a knot in a closed orientable manifold we define the growth rate of the tunnel number of to be . As o…
Morimoto's Conjecture for m-small knots
Tsuyoshi Kobayashi, Yo'av Rieck
Let be the exterior of connected sum of knots and the exteriors of the individual knots. In \cite{morimoto1} Morimoto conjectured (originally for ) that $g(X) < σ_{i…
Local detection of strongly irreducible Heegaard splittings via knot exteriors
Tsuyoshi Kobayashi, Yo'av Rieck
We study the way a strongly irreducible Heegaard surface intersects a knot exterior embedded in a 3-manifold, and show that if consists of simple closed…
Classification of unknotting tunnels for two bridge knots
Tsuyoshi Kobayashi
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 clas…