Isomorphisms and commensurability of surface Houghton groups

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)90069-8Search 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. Search 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/s00208-023-02751-2Search 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/rnaa229Search 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/rny093Search 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)90015-6Search 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.2019.56Search 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/1214448743Search 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. Search 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.12277Search 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. Search 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. 10.4171/103-1/11Search 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.2022.26.1385Search 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/BF01226445Search 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. Search in Google Scholar

[16] E. Pardo, The isomorphism problem for Higman–Thompson groups, J. Algebra 344 (2011), 172–183. 10.1016/j.jalgebra.2011.07.026Search in Google Scholar