## 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