TY - JOUR
T1 - Counting genus one fibered knots in lens spaces
AU - Baker, Kenneth L.
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2014/9/1
Y1 - 2014/9/1
N2 - 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.
AB - 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.
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U2 - 10.1307/mmj/1409932633
DO - 10.1307/mmj/1409932633
M3 - Article
AN - SCOPUS:84907057972
VL - 63
SP - 553
EP - 569
JO - Michigan Mathematical Journal
JF - Michigan Mathematical Journal
SN - 0026-2285
IS - 3
ER -