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27 papers · 1 filter
Double branched covers of tunnel number one knots
Yeonhee Jang, Luisa Paoluzzi
We provide criteria ensuring that a tunnel number one knot is not determined by its double branched cover, in the sense that the double branched cover is also the double branch…
The realization problem for Jørgensen numbers
Yasushi Yamashita, Ryosuke Yamazaki
Let G be a two generator subgroup of PSL(2,C). The Jorgensen number J(G) of G is defined by J(G)=inf{ |tr^2 A-4|+|tr[A,B]-2| ; G=<A,B>}. If G is a non-elementary Kleinian group, th…
On keen Heegaard splittings
Ayako Ido, Yeonhee Jang, Tsuyoshi Kobayashi
In this paper, we introduce a new concept of {\it strongly keen} for Heegaard splittings, and show that, for any integers and , there exists a strongly keen Heeg…
Meridional rank and bridge number for a class of links
Michel Boileau, Yeonhee Jang, Richard Weidmann
We prove that links with meridional rank 3 whose 2-fold branched covers are graph manifolds are 3-bridge links. This gives a partial answer to a question by S. Cappell and J. Shane…
The growth rate of the tunnel number of m-small knots
Tsuyoshi Kobayashi, Yo'av Rieck
In a previous paper the authors defined the growth rate of the tunnel number of knots, an invariant that measures that asymptotic behavior of the tunnel number under connected sum.…
A knot with destabilized bridge spheres of arbitrarily high bridge number
Yeonhee Jang, Tsuyoshi Kobayashi, Makoto Ozawa +1
We show that there exists an infinite family of knots, each of which has, for each integer k>=0, a destabilized (2k+5)-bridge sphere. We also show that, for each integer n>=4, ther…