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Transactions of the American Mathematical Society

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Comparing Heegaard splittings
-the bounded case

Authors: Hyam Rubinstein and Martin Scharlemann
Journal: Trans. Amer. Math. Soc. 350 (1998), 689-715
MSC (1991): Primary 57N10; Secondary 57M50
MathSciNet review: 1401528
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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.

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Additional Information

Hyam Rubinstein
Affiliation: Department of Mathematics, University of Melbourne, Parkville, Vic 3052, Australia

Martin Scharlemann
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106

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
Article copyright: © Copyright 1998 American Mathematical Society