Parameterizations of 1-bridge torus knots

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A 1-bridge torus knot in a 3-manifold of genus less than or equal to 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.
Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
Issue Date
2003-06
Language
English
Article Type
Article
Keywords

NUMBER ONE KNOTS; BRAID GROUPS

Citation

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, v.12, no.4, pp.463 - 491

ISSN
0218-2165
URI
http://hdl.handle.net/10203/83520
Appears in Collection
MA-Journal Papers(저널논문)
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