Counting genus one fibered knots in lens spaces

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5 Scopus citations

Abstract

The braid axis of a closed 3-braid lifts to a genus one fibered knot in the double cover of S3branched over the closed braid. Every 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 and up to isotopy 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 m = 4, and at most 1 otherwise. Furthermore, each homeomorphism equivalence class in a lens space is realized by at most two isotopy classes.

Original languageEnglish (US)
Pages (from-to)553-569
Number of pages17
JournalMichigan Mathematical Journal
Volume63
Issue number3
DOIs
StatePublished - Sep 1 2014

ASJC Scopus subject areas

  • Mathematics(all)

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