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

 

Heegaard splittings and singularities of the product map of Morse functions


Author: Kazuto Takao
Journal: Trans. Amer. Math. Soc. 366 (2014), 2209-2226
MSC (2010): Primary 57N10, 57M50, 57R45
Published electronically: October 8, 2013
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Abstract: We give an upper bound for the Reidemeister-Singer distance between two Heegaard splittings in terms of the genera and the number of cusp points of the product map of Morse functions for the splittings. It suggests that a certain development in singularity theory may lead to the best possible bound for the Reidemeister-Singer distance.


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Additional Information

Kazuto Takao
Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Osaka 560-0043 Japan
Address at time of publication: Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526 Japan
Email: kazutotakao@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-06015-1
PII: S 0002-9947(2013)06015-1
Keywords: Heegaard splittings, stabilization, Morse function, singular set
Received by editor(s): January 3, 2012
Received by editor(s) in revised form: August 27, 2012
Published electronically: October 8, 2013
Article copyright: © Copyright 2013 American Mathematical Society