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The compression body
graph has infinite diameter
Joseph Maher and Saul Schleimer |
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Algebraic & Geometric Topology 21 (2021) 1817–1856
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Abstract |
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We show that the compression body graph, which is Gromov hyperbolic, has infinite diameter. Furthermore, every subgroup in the Johnson filtration of the mapping class group contains elements which act loxodromically on the compression body graph. Our methods give an alternative proof of a result of Biringer, Johnson and Minsky: the stable lamination of a pseudo-Anosov element is contained in the limit set of a compression body if and only if some power of the pseudo-Anosov element extends over a nontrivial subcompression body. We also extend results of Lubotzky, Maher and Wu, on the distribution of Casson invariants of random Heegaard splittings, to a larger class of random walks. |
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Keywords
curve complex, disc set, handlebody, compression body
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Mathematical Subject Classification 2010
Primary: 37E30
Secondary: 20F65, 57M50
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References |
Publication
Received: 7 October 2019
Revised: 3 July 2020
Accepted: 19 July 2020
Published: 18 August 2021
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Authors |
| Joseph Maher | |
| Department of Mathematics CUNY College of Staten Island and CUNY Graduate Center Staten Island, NY United States |
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| Saul Schleimer | |
| Mathematics Institute University of Warwick Coventry United Kingdom |
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