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

Volume 26
Issue 5, 1597–1963
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
Asymptotic translation lengths and normal generation for pseudo-Anosov monodromies of fibered $3$–manifolds

Hyungryul Baik, Eiko Kin, Hyunshik Shin and Chenxi Wu

Algebraic & Geometric Topology 23 (2023) 1363–1398
Bibliography
1 T Aougab, S J Taylor, Pseudo-Anosovs optimizing the ratio of Teichmüller to curve graph translation length, from: "In the tradition of Ahlfors–Bers, VII" (editors A S Basmajian, Y N Minsky, A W Reid), Contemp. Math. 696, Amer. Math. Soc. (2017) 17 MR3715439
2 H Baik, H Shin, Minimal asymptotic translation lengths of Torelli groups and pure braid groups on the curve graph, Int. Math. Res. Not. 2020 (2020) 9974 MR4190393
3 H Baik, H Shin, C Wu, An upper bound on the asymptotic translation lengths on the curve graph and fibered faces, Indiana Univ. Math. J. 70 (2021) 1625 MR4318485
4 M Bestvina, M Handel, Train-tracks for surface homeomorphisms, Topology 34 (1995) 109 MR1308491
5 B H Bowditch, Tight geodesics in the curve complex, Invent. Math. 171 (2008) 281 MR2367021
6 D Calegari, Foliations and the geometry of 3–manifolds, Oxford Univ. Press (2007) MR2327361
7 B Farb, C J Leininger, D Margalit, The lower central series and pseudo-Anosov dilatations, Amer. J. Math. 130 (2008) 799 MR2418928
8 B Farb, D Margalit, A primer on mapping class groups, 49, Princeton Univ. Press (2012) MR2850125
9 A Fathi, F Laudenbach, V Poénaru, editors, Travaux de Thurston sur les surfaces, 66–67, Soc. Math. France (1979) 284 MR568308
10 D Fried, Flow equivalence, hyperbolic systems and a new zeta function for flows, Comment. Math. Helv. 57 (1982) 237 MR684116
11 D Fried, The geometry of cross sections to flows, Topology 21 (1982) 353 MR670741
12 V Gadre, E Hironaka, R P Kent IV, C J Leininger, Lipschitz constants to curve complexes, Math. Res. Lett. 20 (2013) 647 MR3188024
13 V Gadre, C Y Tsai, Minimal pseudo-Anosov translation lengths on the complex of curves, Geom. Topol. 15 (2011) 1297 MR2825314
14 N V Ivanov, Fifteen problems about the mapping class groups, from: "Problems on mapping class groups and related topics" (editor B Farb), Proc. Sympos. Pure Math. 74, Amer. Math. Soc. (2006) 71 MR2264532
15 E Kin, Dynamics of the monodromies of the fibrations on the magic 3–manifold, New York J. Math. 21 (2015) 547 MR3386537
16 E Kin, H Shin, Small asymptotic translation lengths of pseudo-Anosov maps on the curve complex, Groups Geom. Dyn. 13 (2019) 883 MR4002221
17 E Kin, M Takasawa, Pseudo-Anosov braids with small entropy and the magic 3–manifold, Comm. Anal. Geom. 19 (2011) 705 MR2880213
18 M Korkmaz, A Papadopoulos, On the arc and curve complex of a surface, Math. Proc. Cambridge Philos. Soc. 148 (2010) 473 MR2609303
19 M Landry, Stable loops and almost transverse surfaces, Groups Geom. Dyn. 17 (2023) 35 MR4563328
20 J Lanier, D Margalit, Normal generators for mapping class groups are abundant, preprint (2018)
21 D D Long, A note on the normal subgroups of mapping class groups, Math. Proc. Cambridge Philos. Soc. 99 (1986) 79 MR809501
22 D D Long, U Oertel, Hyperbolic surface bundles over the circle, from: "Progress in knot theory and related topics" (editors M Boileau, M Domergue, Y Mathieu, K Millett), Travaux en Cours 56, Hermann (1997) 121 MR1603150
23 J Maher, G Tiozzo, Random walks, WPD actions, and the Cremona group, Proc. Lond. Math. Soc. 123 (2021) 153 MR4307033
24 H A Masur, Y N Minsky, Geometry of the complex of curves, I : Hyperbolicity, Invent. Math. 138 (1999) 103 MR1714338
25 H A Masur, Y N Minsky, Geometry of the complex of curves, II : Hierarchical structure, Geom. Funct. Anal. 10 (2000) 902 MR1791145
26 S Matsumoto, Topological entropy and Thurston’s norm of atoroidal surface bundles over the circle, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 34 (1987) 763 MR927609
27 C T McMullen, Polynomial invariants for fibered 3–manifolds and Teichmüller geodesics for foliations, Ann. Sci. École Norm. Sup. 33 (2000) 519 MR1832823
28 L Mosher, Surfaces and branched surfaces transverse to pseudo-Anosov flows on 3–manifolds, J. Differential Geom. 34 (1991) 1 MR1114450
29 A Papadopoulos, R C Penner, A characterization of pseudo-Anosov foliations, Pacific J. Math. 130 (1987) 359 MR914107
30 S Schleimer, Strongly irreducible surface automorphisms, from: "Topology and geometry of manifolds" (editors G Matić, C McCrory), Proc. Sympos. Pure Math. 71, Amer. Math. Soc. (2003) 287 MR2024639
31 B Strenner, Fibrations of 3–manifolds and asymptotic translation length in the arc complex, preprint (2018) arXiv:1810.07236
32 W P Thurston, A norm for the homology of 3–manifolds, 339, Amer. Math. Soc. (1986) 99 MR823443
33 W P Thurston, Entropy in dimension one, from: "Frontiers in complex dynamics" (editors A Bonifant, M Lyubich, S Sutherland), Princeton Math. Ser. 51, Princeton Univ. Press (2014) 339 MR3289916
34 A D Valdivia, Asymptotic translation length in the curve complex, New York J. Math. 20 (2014) 989 MR3291608
35 A D Valdivia, Lipschitz constants to curve complexes for punctured surfaces, Topology Appl. 216 (2017) 137 MR3584129