Isomorphisms and commensurability of surface Houghton groups
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Javier Aramayona
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Christopher J. Leininger
Abstract
We classify surface Houghton groups, as well as their pure subgroups, up to isomorphism, commensurability, and quasi-isometry.
Funding source: Agencia Estatal de Investigación
Award Identifier / Grant number: PID2021-126254NB-I00
Award Identifier / Grant number: CEX2019-000904-S
Funding source: National Science Foundation
Award Identifier / Grant number: DMS-2303262
Award Identifier / Grant number: DMS-2305286
Funding statement: J. Aramayona was supported by grant PID2021-126254NB-I00 and by the Severo Ochoa award CEX2019-000904-S, funded by MCIN/AEI/10.13039/501100011033. G. Domat was supported by NSF DMS-2303262. C. J. Leininger was supported by NSF DMS-2305286.
Acknowledgements
J. Aramayona is grateful to Rice University, and particularly to C. J. Leininger, for their hospitality. The authors are grateful to Anthony Genevois for pointing out Corollary 1.3.
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Communicated by: Rachel Skipper
References
[1] J. M. Alonso, Finiteness conditions on groups and quasi-isometries, J. Pure Appl. Algebra 95 (1994), no. 2, 121–129. 10.1016/0022-4049(94)90069-8Suche in Google Scholar
[2] J. Aramayona, K.-U. Bux, J. Flechsig, N. Petrosyan and X. Wu, Asymptotic mapping class groups of Cantor manifolds and their finiteness properties, preprint (2021), https://arxiv.org/abs/2110.05318. Suche in Google Scholar
[3] J. Aramayona, K.-U. Bux, H. Kim and C. J. Leininger, Surface Houghton groups, Math. Ann. (2023), 10.1007/s00208-023-02751-2. 10.1007/s00208-023-02751-2Suche in Google Scholar
[4] J. Aramayona, P. Patel and N. G. Vlamis, The first integral cohomology of pure mapping class groups, Int. Math. Res. Not. IMRN 2020 (2020), no. 22, 8973–8996. 10.1093/imrn/rnaa229Suche in Google Scholar
[5] J. Bavard, S. Dowdall and K. Rafi, Isomorphisms between big mapping class groups, Int. Math. Res. Not. IMRN 2020 (2020), no. 10, 3084–3099. 10.1093/imrn/rny093Suche in Google Scholar
[6] K. S. Brown, Finiteness properties of groups, J. Pure. Appl. Algebra 44 (1987), no. 1–3, 45–75. 10.1016/0022-4049(87)90015-6Suche in Google Scholar
[7] J. Cantwell, L. Conlon and S. R. Fenley, Endperiodic automorphisms of surfaces and foliations, Ergodic Theory Dynam. Systems 41 (2021), no. 1, 66–212. 10.1017/etds.2019.56Suche in Google Scholar
[8] S. R. Fenley, Asymptotic properties of depth one foliations in hyperbolic 3-manifolds, J. Differential Geom. 36 (1992), no. 2, 269–313. 10.4310/jdg/1214448743Suche in Google Scholar
[9] E. Field, A. Kent, C. Leininger and M. Loving, A lower bound on volumes of end-periodic mapping tori, preprint (2023), https://arxiv.org/abs/2306.03279. Suche in Google Scholar
[10] E. Field, H. Kim, C. Leininger and M. Loving, End-periodic homeomorphisms and volumes of mapping tori, J. Topol. 16 (2023), no. 1, 57–105. 10.1112/topo.12277Suche in Google Scholar
[11] L. Funar, Braided Houghton groups as mapping class groups, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N. S.) 53 (2007), no. 2, 229–240. Suche in Google Scholar
[12] L. Funar, C. Kapoudjian and V. Sergiescu, Asymptotically rigid mapping class groups and Thompson’s groups, Handbook of Teichmüller Theory. Volume III, IRMA Lect. Math. Theor. Phys. 17, European Mathematical Society, Zürich (2012), 595–664. 10.4171/103-1/11Suche in Google Scholar
[13] A. Genevois, A. Lonjou and C. Urech, Asymptotically rigid mapping class groups, I: Finiteness properties of braided Thompson’s and Houghton’s groups, Geom. Topol. 26 (2022), no. 3, 1385–1434. 10.2140/gt.2022.26.1385Suche in Google Scholar
[14] C. H. Houghton, The first cohomology of a group with permutation module coefficients, Arch. Math. (Basel) 31 (1978/79), no. 3, 254–258. 10.1007/BF01226445Suche in Google Scholar
[15] M. P. Landry, Y. N. Minsky and S. J. Taylor, Endperiodic maps via pseudo-Anosov flows, preprint (2023), https://arxiv.org/abs/2304.10620. Suche in Google Scholar
[16] E. Pardo, The isomorphism problem for Higman–Thompson groups, J. Algebra 344 (2011), 172–183. 10.1016/j.jalgebra.2011.07.026Suche in Google Scholar
© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- The relational complexity of linear groups acting on subspaces
- Cliques in derangement graphs for innately transitive groups
- Representation zeta function of a family of maximal class groups: Non-exceptional primes
- Character degrees of 5-groups of maximal class
- Automorphic word maps and the Amit–Ashurst conjecture
- Groups with subnormal or modular Schmidt 𝑝𝑑-subgroups
- Finite normal subgroups of strongly verbally closed groups
- The central tree property and algorithmic problems on subgroups of free groups
- Uniqueness of roots up to conjugacy in circular and hosohedral-type Garside groups
- Isomorphisms and commensurability of surface Houghton groups
Artikel in diesem Heft
- Frontmatter
- The relational complexity of linear groups acting on subspaces
- Cliques in derangement graphs for innately transitive groups
- Representation zeta function of a family of maximal class groups: Non-exceptional primes
- Character degrees of 5-groups of maximal class
- Automorphic word maps and the Amit–Ashurst conjecture
- Groups with subnormal or modular Schmidt 𝑝𝑑-subgroups
- Finite normal subgroups of strongly verbally closed groups
- The central tree property and algorithmic problems on subgroups of free groups
- Uniqueness of roots up to conjugacy in circular and hosohedral-type Garside groups
- Isomorphisms and commensurability of surface Houghton groups
