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Networking Seifert
surgeries on knots, III
Arnaud Deruelle, Katura Miyazaki and Kimihiko Motegi |
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Algebraic & Geometric Topology 14 (2014) 2065–2101
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Abstract |
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How do Seifert surgeries on hyperbolic knots arise from those on torus knots? We approach this question from a networking viewpoint introduced by the authors in [Mem. Amer. Math. Soc. 217 (2012), no. 1021]. The Seifert surgery network is a –dimensional complex whose vertices correspond to Seifert surgeries; two vertices are connected by an edge if one Seifert surgery is obtained from the other by a single twist along a trivial knot called a seiferter or along an annulus cobounded by seiferters. Successive twists along a “hyperbolic seiferter” or a “hyperbolic annular pair” produce infinitely many Seifert surgeries on hyperbolic knots. In this paper, we investigate Seifert surgeries on torus knots that have hyperbolic seiferters or hyperbolic annular pairs, and obtain results suggesting that such surgeries are restricted. |
Keywords
Dehn surgery, hyperbolic knot, Seifert fiber space,
seiferter, Seifert surgery network, band-sum
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Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 57M50, 57N10
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References |
Publication
Received: 8 November 2012
Revised: 8 November 2013
Accepted: 17 November 2013
Published: 28 August 2014
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Authors |
| Arnaud Deruelle | |
| Institute of Natural Sciences Nihon University 3-25-40 Sakurajosui, Setagaya-ku Tokyo 156-8550 Japan |
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| Katura Miyazaki | |
| Faculty of Engineering Tokyo Denki University 5 Senju-Asahi-cho, Adachi-ku Tokyo 120-8551 Japan |
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| Kimihiko Motegi | |
| Department of Mathematics Nihon University 3-25-40 Sakurajosui, Setagaya-ku Tokyo 156-8550 Japan |
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| http://www.math.chs.nihon-u.ac.jp/~motegi/ | |
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