Heegaard splittings and singularities of the product map of Morse functions
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- by Kazuto Takao PDF
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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.References
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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
- Received by editor(s): January 3, 2012
- Received by editor(s) in revised form: August 27, 2012
- Published electronically: October 8, 2013
- © Copyright 2013 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 366 (2014), 2209-2226
- MSC (2010): Primary 57N10, 57M50, 57R45
- DOI: https://doi.org/10.1090/S0002-9947-2013-06015-1
- MathSciNet review: 3152728