Dehn surgeries on knots which yield lens spaces and genera of knots
Use this link to cite this item : https://ir.lib.hiroshima-u.ac.jp/00014107
ID | 14107 |
file | |
creator |
Goda, Hiroshi
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NDC |
Mathematics
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abstract | It is an interesting open question when Dehn surgery on a knot in the 3-sphere S3 can produce a lens space (see [10, 12]). Some studies have been made for special knots; in particular, the question is completely solved for torus knots [21] and satellite knots [3, 29, 31]. It is known that there are many examples of hyperbolic knots which admit Dehn surgeries yielding lens spaces. For example, Fintushel and Stern [8] have shown that 18- and 19-surgeries on the ([minus sign]2, 3, 7)-pretzel knot give lens spaces L(18, 5) and L(19, 7), respectively. However, there seems to be no essential progress on hyperbolic knots. It might be a reason that some famous classes of hyperbolic knots, such as 2-bridge knots [26], alternating knots [5], admit no surgery yielding lens spaces.In this paper we focus on the genera of knots to treat the present condition methodically and show that there is a constraint on the order of the fundamental group of the resulting lens space obtained by Dehn surgery on a hyperbolic knot. Also, this new standpoint enables us to present a conjecture concerning such a constraint, which holds for all known examples.
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journal title |
Mathematical proceedings of the Cambridge Philosophical Society
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volume | Volume 129
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issue | Issue 3
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start page | 501
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end page | 515
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date of issued | 2000
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publisher | Cambridge University Press
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issn | 0305-0041
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publisher doi | |
language |
eng
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nii type |
Journal Article
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HU type |
Journal Articles
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DCMI type | text
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format | application/pdf
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text version | publisher
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rights | Copyright (c) 2000 Cambridge University Press
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relation is version of URL | http://dx.doi.org/10.1017/S0305004100004692
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department |
Graduate School of Education
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