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Comparing Heegaard splittings -the bounded case

Author(s): Hyam Rubinstein; Martin Scharlemann
Journal: Trans. Amer. Math. Soc. 350 (1998), 689-715.
MSC (1991): Primary 57N10; Secondary 57M50
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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
Email: rubin@mundoe.mu.oz.au

Martin Scharlemann
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
Email: mgscharl@math.ucsb.edu

DOI: 10.1090/S0002-9947-98-01824-8
PII: S 0002-9947(98)01824-8
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 of article: Copyright 1998, American Mathematical Society

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