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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 11 scientific papers (total in 11 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
Full-text PDF (332 kB) Citations (11)
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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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\vol 292
\pages 124--148
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    • This publication is cited in the following 11 articles:
    1. Anna Roig-Sanchis, “The length spectrum of random hyperbolic 3-manifolds”, Advances in Mathematics, 466 (2025), 110158  crossref
    2. Will Sawin, Melanie Matchett Wood, “Finite quotients of 3-manifold groups”, Invent. math., 237:1 (2024), 349  crossref
    3. Will Sawin, Melanie Matchett Wood, “Publisher Correction to: Finite quotients of 3-manifold groups”, Invent. math., 237:1 (2024), 441  crossref
    4. Chaim Even-Zohar, Joel Hass, “Random colorings in manifolds”, Isr. J. Math., 256:1 (2023), 153  crossref
    5. Ursula Hamenstädt, Gabriele Viaggi, “Small eigenvalues of random 3-manifolds”, Trans. Amer. Math. Soc., 375:6 (2022), 3795  crossref
    6. J. Maher, S. Schleimer, “The compression body graph has infinite diameter”, Algebr. Geom. Topol., 21:4 (2021), 1817–1856  crossref  mathscinet  isi  scopus
    7. G. Viaggi, “Volumes of Random 3-manifolds”, J. Topol., 14:2 (2021), 504–537  crossref  mathscinet  isi  scopus
    8. A. Sisto, “Many haken heegaard splittings”, J. Topol. Anal., 12:2 (2020), 357–369  crossref  mathscinet  zmath  isi
    9. M. H. Sunderland, “Linear progress with exponential decay in weakly hyperbolic groups”, Group. Geom. Dyn., 14:2 (2020), 539–566  crossref  mathscinet  zmath  isi
    10. A. V. Malyutin, “On the question of genericity of hyperbolic knots”, Int. Math. Res. Notices, 2020:21 (2020), 7792–7828  crossref  mathscinet  isi
    11. Chaim Even-Zohar, “Models of random knots”, J Appl. and Comput. Topology, 1:2 (2017), 263  crossref
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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