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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Taut foliations in branched cyclic covers and left-orderable groups
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by Steven Boyer and Ying Hu PDF
Trans. Amer. Math. Soc. 372 (2019), 7921-7957 Request permission


We study the left-orderability of the fundamental groups of cyclic branched covers of links which admit co-oriented taut foliations. In particular we do this for cyclic branched covers of fibred knots in integer homology $3$-spheres and cyclic branched covers of closed braids. The latter allows us to complete the proof of the L-space conjecture for closed, connected, orientable, irreducible $3$-manifolds containing a genus one fibred knot. We also prove that the universal abelian cover of a manifold obtained by generic Dehn surgery on a hyperbolic fibred knot in an integer homology $3$-sphere admits a co-oriented taut foliation and has left-orderable fundamental group, even if the surgered manifold does not, and that the same holds for many branched covers of satellite knots with braided patterns. A key fact used in our proofs is that the Euler class of a universal circle representation associated to a co-oriented taut foliation coincides with the Euler class of the foliation’s tangent bundle. Though known to experts, no proof of this important result has appeared in the literature. We provide such a proof in the paper.
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Additional Information
  • Steven Boyer
  • Affiliation: Département de Mathématiques, Université du Québec à Montréal, 201 avenue du Président-Kennedy, Montréal, Quebec H2X 3Y7, Canada
  • MR Author ID: 219677
  • Email:
  • Ying Hu
  • Affiliation: Department of Mathematics, University of Nebraska Omaha, 6001 Dodge Street, Omaha, Nebraska 68182
  • Email:
  • Received by editor(s): June 19, 2018
  • Received by editor(s) in revised form: February 18, 2019, and February 22, 2019
  • Published electronically: June 10, 2019
  • Additional Notes: The first author was partially supported by NSERC grant RGPIN 9446-2013
    The second author was partially supported by a CIRGET postdoctoral fellowship
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 372 (2019), 7921-7957
  • MSC (2010): Primary 57M50, 57R30, 20F60; Secondary 57M25, 57M99, 20F36
  • DOI:
  • MathSciNet review: 4029686