Výsledky vyhledávání - "Takao, Kazuto"

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Diagrammatic criteria for strong irreducibility of Heegaard splittings and finiteness of Goeritz groups

Autor: Koda, Yuya, Takao, Kazuto

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 in addition that the Goeritz group is finite. They are generalizations

Externí odkaz: http://arxiv.org/abs/2402.06849

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A knot with destabilized bridge spheres of arbitrarily high bridge number

Autor: Jang, Yeonhee, Kobayashi, Tsuyoshi, Ozawa, Makoto, Takao, Kazuto

Publikováno v: J. London Math. Soc. (2) 93 (2016), no. 2, 379--396

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, there exists a knot with a destabilized 3-bridge sphere and a destabilized

Externí odkaz: http://arxiv.org/abs/1501.06263

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Lips and swallow-tails of singularities of product maps

Autor: Takao, Kazuto

Publikováno v: J. Singul. 10 (2014), 286--295

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 3-manifold can be realized by isotopies of the functions.
Commen

Externí odkaz: http://arxiv.org/abs/1305.1168

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Heegaard splittings and singularities of the product map of Morse functions

Autor: Takao, Kazuto

Publikováno v: Trans. Amer. Math. Soc. 366 (2014), no. 4, 2209--2226

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 functions for the splittings. It suggests that a certain development in singu

Externí odkaz: http://arxiv.org/abs/1205.1206

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A locally minimal, but not globally minimal bridge position of a knot

Autor: Ozawa, Makoto, Takao, Kazuto

Publikováno v: Math. Proc. Cambridge Philos. Soc. 155 (2013), no. 1, 181--190

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 cannot always be simplified so that the bridge number monotonically decre

Externí odkaz: http://arxiv.org/abs/1203.1119

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Bridge decompositions with distances at least two

Autor: Takao, Kazuto

Publikováno v: Hiroshima Math. J. 42 (2012), no. 2, 161--168

For n-bridge decompositions of links in S^3, we propose a practical method to ensure that the Hempel distance is at least two.
Comment: 7 pages, 5 figures

Externí odkaz: http://arxiv.org/abs/1106.0963

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A refinement of Johnson's bounding for the stable genera of Heegaard splittings

Autor: Takao, Kazuto

Publikováno v: Osaka J. Math. 48 (2011), no. 1, 251-268

For each integer k > 1, Johnson gave a 3-manifold with Heegaard splittings of genera 2k and 2k-1 such that any common stabilization of these two surfaces has genus at least 3k-1. We modify his argument to produce a 3-manifold with two Heegaard spliti

Externí odkaz: http://arxiv.org/abs/1005.1467

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