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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Stable functions and common stabilizations of Heegaard splittings


Author: Jesse Johnson
Journal: Trans. Amer. Math. Soc. 361 (2009), 3747-3765
MSC (2000): Primary 57Mxx
Published electronically: March 4, 2009
MathSciNet review: 2491898
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Abstract: We present a new proof of Reidemeister and Singer's Theorem that any two Heegaard splittings of the same 3-manifold have a common stabilization. The proof leads to an upper bound on the minimal genus of a common stabilization in terms of the number of negative slope inflection points and type two cusps in a Rubinstein-Scharlemann graphic for the two splittings.


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Additional Information

Jesse Johnson
Affiliation: Department of Mathematics, Yale University, New Haven, Connecticut 06520
Email: jessee.johnson@yale.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04731-X
PII: S 0002-9947(09)04731-X
Keywords: Heegaard splitting, stabilization, Rubinstein-Scharlemann graphic
Received by editor(s): May 30, 2007
Published electronically: March 4, 2009
Additional Notes: This research was supported by NSF MSPRF grant 0602368
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.