Parameterizations of 1-Bridge Torus Knots
2003 ◽
Vol 12
(04)
◽
pp. 463-491
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Keyword(s):
A 1-bridge torus knot in a 3-manifold of genus ≤ 1 is a knot drawn on a Heegaard torus with one bridge. We give two types of normal forms to parameterize the family of 1-bridge torus knots that are similar to the Schubert's normal form and the Conway's normal form for 2-bridge knots. For a given Schubert's normal form we give algorithms to determine the number of components and to compute the fundamental group of the complement when the normal form determines a knot. We also give a description of the double branched cover of an ambient 3-manifold branched along a 1-bridge torus knot by using its Conway's normal form and obtain an explicit formula for the first homology of the double cover.
1995 ◽
Vol 117
(1)
◽
pp. 129-135
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2019 ◽
Vol 28
(03)
◽
pp. 1950019
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2016 ◽
Vol 25
(06)
◽
pp. 1650030
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Keyword(s):
1991 ◽
Vol 33
(2)
◽
pp. 125-128
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Keyword(s):
Keyword(s):
1996 ◽
Vol 04
(04)
◽
pp. 331-349
◽
2011 ◽
Vol 20
(12)
◽
pp. 1723-1739
◽
Keyword(s):
2008 ◽
Vol 17
(01)
◽
pp. 13-23
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