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ID 14107
file
creator
Goda, Hiroshi
NDC
Mathematics
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.
journal title
Mathematical proceedings of the Cambridge Philosophical Society
volume
Volume 129
issue
Issue 3
start page
501
end page
515
date of issued
2000
publisher
Cambridge University Press
issn
0305-0041
publisher doi
language
eng
nii type
Journal Article
HU type
Journal Articles
DCMI type
text
format
application/pdf
text version
publisher
rights
Copyright (c) 2000 Cambridge University Press
relation is version of URL
http://dx.doi.org/10.1017/S0305004100004692
department
Graduate School of Education