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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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Comparing 2-handle additions to a genus 2 boundary component
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by Scott A. Taylor PDF
Trans. Amer. Math. Soc. 366 (2014), 3747-3769 Request permission

Abstract:

We prove that knots obtained by attaching a band to a split link satisfy the cabling conjecture. We also give new proofs that unknotting number one knots are prime and that genus is superadditive under a band sum. Additionally, we prove a collection of results comparing two 2-handle additions to a genus 2 boundary component of a compact, orientable 3-manifold. These results give a near complete solution to a conjecture of Scharlemann and provide evidence for a conjecture of Scharlemann and Wu. The proofs make use of a new theorem concerning the effects of attaching a 2-handle to a suture in the boundary of a sutured manifold.
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Additional Information
  • Scott A. Taylor
  • Affiliation: Department of Mathematics and Statistics, Colby College, Waterville, Maine 04901
  • Email: sataylor@colby.edu
  • Received by editor(s): November 3, 2011
  • Received by editor(s) in revised form: October 12, 2012
  • Published electronically: March 4, 2014
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 366 (2014), 3747-3769
  • MSC (2010): Primary 57M50
  • DOI: https://doi.org/10.1090/S0002-9947-2014-06253-3
  • MathSciNet review: 3192616