Download this article
 Download this article For screen
For printing
Recent Issues

Volume 26
Issue 4, 1229–1596
Issue 3, 825–1227
Issue 2, 411–824
Issue 1, 1–410

Volume 25, 9 issues

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
Infinite-type loxodromic isometries of the relative arc graph

Carolyn Abbott, Nicholas Miller and Priyam Patel

Algebraic & Geometric Topology 25 (2025) 563–644
Bibliography
1 A I o Mathematics, Surfaces of infinite type, problem lists (2019)
2 J Aramayona, A Fossas, H Parlier, Arc and curve graphs for infinite-type surfaces, Proc. Amer. Math. Soc. 145 (2017) 4995 MR3692012
3 J Aramayona, P Patel, N G Vlamis, The first integral cohomology of pure mapping class groups, Int. Math. Res. Not. 2020 (2020) 8973 MR4216709
4 J Aramayona, N G Vlamis, Big mapping class groups: an overview, from: "In the tradition of Thurston : geometry and topology" (editors K Ohshika, A Papadopoulos), Springer (2020) 459 MR4264585
5 J Bavard, Hyperbolicité du graphe des rayons et quasi-morphismes sur un gros groupe modulaire, Geom. Topol. 20 (2016) 491 MR3470720
6 J Bavard, A Genevois, Big mapping class groups are not acylindrically hyperbolic, Math. Slovaca 68 (2018) 71 MR3764317
7 J Bavard, A Walker, The Gromov boundary of the ray graph, Trans. Amer. Math. Soc. 370 (2018) 7647 MR3852444
8 J Bavard, A Walker, Two simultaneous actions of big mapping class groups, Trans. Amer. Math. Soc. 376 (2023) 7603 MR4657217
9 M Bestvina, K Bromberg, K Fujiwara, Constructing group actions on quasi-trees and applications to mapping class groups, Publ. Math. Inst. Hautes Études Sci. 122 (2015) 1 MR3415065
10 M Bestvina, K Fujiwara, Bounded cohomology of subgroups of mapping class groups, Geom. Topol. 6 (2002) 69 MR1914565
11 F Bonahon, Closed curves on surfaces, preprint (2000)
12 D Calegari, Big mapping class groups and dynamics, blog post (2009)
13 J Cantwell, L Conlon, S R Fenley, Endperiodic automorphisms of surfaces and foliations, Ergodic Theory Dynam. Systems 41 (2021) 66 MR4190052
14 F Fournier-Facio, Y Lodha, M C B Zaremsky, Braided Thompson groups with and without quasimorphisms, Algebr. Geom. Topol. 24 (2024) 1601 MR4767881
15 S Hensel, P Przytycki, R C H Webb, 1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs, J. Eur. Math. Soc. 17 (2015) 755 MR3336835
16 W P Hooper, The invariant measures of some infinite interval exchange maps, Geom. Topol. 19 (2015) 1895 MR3375521
17 B von Kerékjártó, Vorlesungen über Topologie, I : Flächentoplogie, Springer (1923)
18 J Lanier, M Loving, Centers of subgroups of big mapping class groups and the Tits alternative, Glas. Mat. Ser. III 55(75) (2020) 85 MR4115214
19 W B R Lickorish, A representation of orientable combinatorial 3-manifolds, Ann. of Math. 76 (1962) 531 MR151948
20 I Morales, F Valdez, Loxodromic elements in big mapping class groups via the Hooper–Thurston–Veech construction, Algebr. Geom. Topol. 22 (2022) 3809 MR4562559
21 J Nielsen, Surface transformation classes of algebraically finite type, 2, Munksgaard (1944) 89 MR15791
22 P Patel, N G Vlamis, Algebraic and topological properties of big mapping class groups, Algebr. Geom. Topol. 18 (2018) 4109 MR3892241
23 R C Penner, J L Harer, Combinatorics of train tracks, 125, Princeton Univ. Press (1992) MR1144770
24 A J Rasmussen, WWPD elements of big mapping class groups, Groups Geom. Dyn. 15 (2021) 825 MR4322013
25 I Richards, On the classification of noncompact surfaces, Trans. Amer. Math. Soc. 106 (1963) 259 MR143186
26 D Šarić, Train tracks and measured laminations on infinite surfaces, Trans. Amer. Math. Soc. 374 (2021) 8903 MR4337933
27 W P Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. 19 (1988) 417 MR956596
28 Y Verberne, A construction of pseudo-Anosov homeomorphisms using positive twists, Algebr. Geom. Topol. 23 (2023) 1601 MR4602409