2013 Fiscal Year Final Research Report
Networking Seifert surgeries on knots
| Project/Area Number |
21540098
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Nihon University |
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Principal Investigator |
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Keywords | 幾何学 / トポロジー / 結び目 / ３次元多様体 / Dehn手術 / Seifert fiber space / seiferter / Seifert Surgery Network |
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| Research Abstract |
How do Seifert surgeries on hyperbolic knots arise from those on torus knots? We approach this question from a networking viewpoint. Our basic idea is finding relationships among such surgeries using ``inheritance" property of seiferters. A path in the network from one Seifert surgery to another explains how the former Seifert surgery is obtained from the latter after a sequence of twistings along seiferters and/or annuli cobounded by pairs of seiferters. We find explicit paths from various known Seifert surgeries to those on torus knots, the most basic and well-understood Seifert surgeries. Successive twists along a ``hyperbolic seiferter" or a ``hyperbolic annular pair" produce infinitely many Seifert surgeries on hyperbolic knots. We have given a list of Seifert surgeries on torus knots which have hyperbolic seiferters or hyperbolic annular pairs, and obtained results suggesting that such surgeries are restricted.
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[Presentation] Networking Seifert surgeries on knots2009
Author(s)
K.Motegi
Organizer
AMS Sectional Meeting, 2009 Fall Western Section Meeting (November 7-8, 2009), Special Session on Knotting Around Dimension Three : A Special Session in Memory of Xiao-Song Lin
Place of Presentation
University of California, Riverside(USA)
Year and Date
2009-11-07
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