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The compression body graph has infinite diameter
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Maher, Joseph and Schleimer, Saul (2021) The compression body graph has infinite diameter. Algebraic & Geometric Topology, 21 . pp. 1817-1856. doi:10.2140/agt.2021.21.1817 ISSN 1472-2747.
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Official URL: https://doi.org/10.2140/agt.2021.21.1817
Abstract
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.
| Item Type: | Journal Article | |||||||||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||||||||
| Library of Congress Subject Headings (LCSH): | Curves, Geometry, Hyperbolic, Random walks (Mathematics) | |||||||||||||||
| Journal or Publication Title: | Algebraic & Geometric Topology | |||||||||||||||
| Publisher: | Mathematical Sciences Publishers | |||||||||||||||
| ISSN: | 1472-2747 | |||||||||||||||
| Official Date: | 18 August 2021 | |||||||||||||||
| Dates: |
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| Volume: | 21 | |||||||||||||||
| Page Range: | pp. 1817-1856 | |||||||||||||||
| DOI: | 10.2140/agt.2021.21.1817 | |||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||
| Publication Status: | Published | |||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||
| Date of first compliant deposit: | 12 October 2020 | |||||||||||||||
| Date of first compliant Open Access: | 2 September 2021 | |||||||||||||||
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