3 citations · 4 across the 4 of their papers we have counts for
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Knot exteriors with additive Heegaard genus and Morimoto's Conjecture
Tsuyoshi Kobayashi, Yo'av Rieck
Given integers g_i > 1 (i=1,...,n) we prove that there exist infinitely may knots K_i in S^3 so that g(E(K_i)) = g_i and the Heegaard genus of the exterior of the connected sum of…
Knots with g(E(K)) = 2 and g(E(K#K#K)) = 6 and Morimoto's Conjecture
Tsuyoshi Kobayashi, Yo'av Rieck
We show that there exist knots K in S^3 with g(E(K))=2 and g(E(K#K#K))=6. Together with Theorem~1.5 of [1], this proves existence of counterexamples to Morimoto's Conjecture (Conje…
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…