Counting genus one fibered knots in lens spaces

Details Counting genus one fibered knots in lens spaces Counting genus one fibered knots in lens spaces

2005-10-18

arxiv.org/abs/math/0510391v4

Mathematics

Geometric Topology

10 pages, 4 figures. V4: Fixed cosmetic errors, slight modification to proof of Thm 2.4

Scientific paper

The braid axis of a closed 3-braid lifts to a genus one fibered knot in the double cover of S^3 branched over the closed braid. Every (null homologous) genus one fibered knot in a 3-manifold may be obtained in this way. Using this perspective we answer a question of Morimoto about the number of genus one fibered knots in lens spaces. We determine the number of genus one fibered knots up to homeomorphism in any given lens space. This number is 3 in the case of the lens space L(4,1), 2 for the lens spaces L(m,1) with m>0, and at most 1 otherwise.

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