Y. Rieck

activity

20022006

most citedOn the growth rate of tunnel number of knots

3 citations · 5 across the 6 of their papers we have counts for

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4 papers · 1 filter

math.GT2005★ 1 cited

Heegaard genus of the connected sum of m-small knots

Tsuyoshi Kobayashi, Yo'av Rieck

We prove that if $K_{1} \subset M_{1}, ..., K_{n} \subset M_{n}$ 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…

math.GT2004★ 3 cited

On the growth rate of tunnel number of knots

Tsuyoshi Kobayashi, Yo'av Rieck

Given a knot $K$ in a closed orientable manifold $M$ we define the growth rate of the tunnel number of $K$ to be $g r_{t} (K) = lim sup_{n \to \infty} \frac{t ( n K ) - n t ( K )}{n - 1}$ . As o…

math.GT2002

Morimoto's Conjecture for m-small knots

Tsuyoshi Kobayashi, Yo'av Rieck

Let $X$ be the exterior of connected sum of knots and $X_{i}$ the exteriors of the individual knots. In \cite{morimoto1} Morimoto conjectured (originally for $n = 2$ ) that $g(X) < σ_{i…

math.GT2002

Local detection of strongly irreducible Heegaard splittings via knot exteriors

Tsuyoshi Kobayashi, Yo'av Rieck

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…