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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 Heegaard splittings -the bounded case
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by Hyam Rubinstein and Martin Scharlemann PDF
Trans. Amer. Math. Soc. 350 (1998), 689-715 Request permission

Abstract:

In a recent paper we used Cerf theory to compare strongly irreducible Heegaard splittings of the same closed irreducible orientable 3-manifold. This captures all irreducible splittings of non-Haken 3-manifolds. One application is a solution to the stabilization problem for such splittings: If $p \leq q$ are the genera of two splittings, then there is a common stabilization of genus $5p + 8q - 9$. Here we show how to obtain similar results even when the 3-manifold has boundary.
References
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Additional Information
  • Hyam Rubinstein
  • Affiliation: Department of Mathematics, University of Melbourne, Parkville, Vic 3052, Australia
  • MR Author ID: 151465
  • Email: rubin@mundoe.mu.oz.au
  • Martin Scharlemann
  • Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
  • MR Author ID: 155620
  • Email: mgscharl@math.ucsb.edu
  • Received by editor(s): December 21, 1995
  • Received by editor(s) in revised form: May 8, 1996
  • Additional Notes: Each author was partially supported by a grant from the Australian Research Council
  • © Copyright 1998 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 689-715
  • MSC (1991): Primary 57N10; Secondary 57M50
  • DOI: https://doi.org/10.1090/S0002-9947-98-01824-8
  • MathSciNet review: 1401528