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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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Irreducible 3-manifolds that cannot be obtained by 0-surgery on a knot
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by Matthew Hedden, Min Hoon Kim, Thomas E. Mark and Kyungbae Park PDF
Trans. Amer. Math. Soc. 372 (2019), 7619-7638 Request permission

Abstract:

We give two infinite families of examples of closed, orientable, irreducible 3-manifolds $M$ such that $b_1(M)=1$ and $\pi _1(M)$ has weight 1, but $M$ is not the result of Dehn surgery along a knot in the 3-sphere. This answers a question of Aschenbrenner, Friedl, and Wilton and provides the first examples of irreducible manifolds with $b_1=1$ that are known not to be surgery on a knot in the 3-sphere. One family consists of Seifert fibered 3-manifolds, while each member of the other family is not even homology cobordant to any Seifert fibered 3-manifold. None of our examples are homology cobordant to any manifold obtained by Dehn surgery along a knot in the 3-sphere.
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Additional Information
  • Matthew Hedden
  • Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
  • MR Author ID: 769768
  • Email: mhedden@math.msu.edu
  • Min Hoon Kim
  • Affiliation: School of Mathematics, Korea Institute for Advanced Study, Seoul 02455, Republic of Korea
  • MR Author ID: 1067137
  • Email: kminhoon@kias.re.kr
  • Thomas E. Mark
  • Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22903
  • MR Author ID: 690723
  • Email: tmark@virginia.edu
  • Kyungbae Park
  • Affiliation: Department of Mathematical Sciences, Seoul National University, Seoul 08826, Republic of Korea
  • MR Author ID: 1124709
  • Email: kyungbaepark@snu.ac.kr
  • Received by editor(s): July 9, 2018
  • Received by editor(s) in revised form: December 18, 2018
  • Published electronically: May 20, 2019
  • Additional Notes: The first author’s work on this project was partially supported by NSF CAREER grant DMS-1150872, DMS-1709016, and an NSF postdoctoral fellowship.
    The second author was partially supported by the POSCO TJ Park Science Fellowship.
    The third author was supported in part by a grant from the Simons Foundation (523795, TM).
    The fourth author was partially supported by Basic Science Research Program through the National Research Foundation of Korea (NRF, F2018R1C1B6008364).
    Kyungbae Park is the corresponding author
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 372 (2019), 7619-7638
  • MSC (2010): Primary 57M25, 57M27, 57R58, 57R65
  • DOI: https://doi.org/10.1090/tran/7786
  • MathSciNet review: 4029676