5 citations · 12 across the 7 of their papers we have counts for
7 papers
Diagrammatic criteria for strong irreducibility of Heegaard splittings and finiteness of Goeritz groups
Yuya Koda, Kazuto Takao
We give two criteria for diagrams of Heegaard splittings of 3-manifolds. Weaker one of them guarantees that the splitting is strongly irreducible, and the stronger one guarantees i…
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…
Lips and swallow-tails of singularities of product maps
Kazuto Takao
Lips and swallow-tails are generic local moves of singularities of a smooth map to a 2-manifold. We prove that these moves of singularities of the product map of two functions on a…
Heegaard splittings and singularities of the product map of Morse functions
Kazuto Takao
We give an upper bound for the Reidemeister-Singer distance between two Heegaard splittings in terms of the genera and the number of cusp points of the product map of Morse functio…
A locally minimal, but not globally minimal bridge position of a knot
Makoto Ozawa, Kazuto Takao
We give a locally minimal, but not globally minimal bridge position of a knot, that is, an unstabilized, nonminimal bridge position of a knot. It implies that a bridge position can…
Bridge decompositions with distances at least two
Kazuto Takao
For n-bridge decompositions of links in S^3, we propose a practical method to ensure that the Hempel distance is at least two.