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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Volume 292, Pages 124–148
DOI: https://doi.org/10.1134/S0371968516010088 (Mi tm3686) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Random methods in 3-manifold theory

Alexander Lubotzkya, Joseph Maherb, Conan Wuc

a Einstein Institute of Mathematics, Hebrew University, Givat Ram, Jerusalem 9190401, Israel
b College of Staten Island and Graduate Center, City University of New York, New York, NY 10314, USA
c Mathematics Department, Princeton University, Princeton, NJ 08544, USA
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DOI: https://doi.org/10.1134/S0371968516010088
Abstract: The surface map arising from a random walk on the mapping class group may be used as the gluing map for a Heegaard splitting, and the resulting 3-manifold is known as a random Heegaard splitting. We show that the splitting distance of random Heegaard splittings grows linearly in the length of the random walk, with an exponential decay estimate for the proportion with slower growth. We use this to obtain the limiting distribution of Casson invariants of random Heegaard splittings.
Funding agency Grant number
European Research Council
National Science Foundation DMS-1006553
Israel Science Foundation
City University of New York TRADB-45-17
Simons Foundation CGM 234477
We acknowledge support by ERC, NSF and ISF. The second author was supported by PSC-CUNY award TRADB-45-17 and Simons Foundation grant CGM 234477. The third author was supported by NSF grant DMS-1006553, and thanks GARE network and the warm hospitality of Hebrew University.
Received: December 9, 2014
English version:
Proceedings of the Steklov Institute of Mathematics, 2016, Volume 292, Pages 118–142
DOI: https://doi.org/10.1134/S0081543816010089
Bibliographic databases:
Document Type: Article
UDC: 519.21+515.162.3
Language: English
Citation: Alexander Lubotzky, Joseph Maher, Conan Wu, “Random methods in 3-manifold theory”, Algebra, geometry, and number theory, Collected papers. Dedicated to Academician Vladimir Petrovich Platonov on the occasion of his 75th birthday, Trudy Mat. Inst. Steklova, 292, MAIK Nauka/Interperiodica, Moscow, 2016, 124–148; Proc. Steklov Inst. Math., 292 (2016), 118–142
Citation in format AMSBIB
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\paper Random methods in 3-manifold theory
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\bookinfo Collected papers. Dedicated to Academician Vladimir Petrovich Platonov on the occasion of his 75th birthday
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\vol 292
\pages 124--148
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    • This publication is cited in the following 10 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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