Volume 19, issue 2 (2019)

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

Volume 25, 1 issue

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
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Least dilatation of pure surface braids

Marissa Loving

Appendix: Marissa Loving and Hugo Parlier

Algebraic & Geometric Topology 19 (2019) 941–964
Bibliography
1 J W Aaber, N Dunfield, Closed surface bundles of least volume, Algebr. Geom. Topol. 10 (2010) 2315 MR2745673
2 I Agol, C J Leininger, D Margalit, Pseudo-Anosov stretch factors and homology of mapping tori, J. Lond. Math. Soc. 93 (2016) 664 MR3509958
3 L V Ahlfors, Lectures on quasiconformal mappings, 38, Amer. Math. Soc. (2006) MR2241787
4 T Aougab, S Huang, Minimally intersecting filling pairs on surfaces, Algebr. Geom. Topol. 15 (2015) 903 MR3342680
5 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
6 H Baik, A Rafiqi, C Wu, Constructing pseudo-Anosov maps with given dilatations, Geom. Dedicata 180 (2016) 39 MR3451455
7 M Bauer, An upper bound for the least dilatation, Trans. Amer. Math. Soc. 330 (1992) 361 MR1094556
8 J S Birman, Mapping class groups and their relationship to braid groups, Comm. Pure Appl. Math. 22 (1969) 213 MR0243519
9 J S Birman, Braids, links, and mapping class groups, 82, Princeton Univ. Press (1974) MR0375281
10 P Buser, Geometry and spectra of compact Riemann surfaces, 106, Birkhäuser (1992) MR1183224
11 S Dowdall, Dilatation versus self-intersection number for point-pushing pseudo-Anosov homeomorphisms, J. Topol. 4 (2011) 942 MR2860347
12 B Farb, C J Leininger, D Margalit, The lower central series and pseudo-Anosov dilatations, Amer. J. Math. 130 (2008) 799 MR2418928
13 B Farb, D Margalit, A primer on mapping class groups, 49, Princeton Univ. Press (2012) MR2850125
14 A Fathi, F Laudenbach, V Poénaru, Thurston’s work on surfaces, 48, Princeton Univ. Press (2012) MR3053012
15 F R Gantmacher, The theory of matrices, I, Chelsea (1959) MR0107649
16 F W Gehring, Quasiconformal mappings which hold the real axis pointwise fixed, from: "Mathematical essays dedicated to A J Macintyre" (editor H Shankar), Ohio Univ. Press (1970) 145 MR0273007
17 J Y Ham, W T Song, The minimum dilatation of pseudo-Anosov 5–braids, Experiment. Math. 16 (2007) 167 MR2339273
18 E Hironaka, Small dilatation mapping classes coming from the simplest hyperbolic braid, Algebr. Geom. Topol. 10 (2010) 2041 MR2728483
19 E Hironaka, E Kin, A family of pseudo-Anosov braids with small dilatation, Algebr. Geom. Topol. 6 (2006) 699 MR2240913
20 S Hirose, E Kin, The asymptotic behavior of the minimal pseudo-Anosov dilatations in the hyperelliptic handlebody groups, Q. J. Math. 68 (2017) 1035 MR3698306
21 Y Imayoshi, M Ito, H Yamamoto, On the Nielsen–Thurston–Bers type of some self-maps of Riemann surfaces with two specified points, Osaka J. Math. 40 (2003) 659 MR2003742
22 N V Ivanov, Subgroups of Teichmüller modular groups, 115, Amer. Math. Soc. (1992) MR1195787
23 E Kin, M Takasawa, Pseudo-Anosovs on closed surfaces having small entropy and the Whitehead sister link exterior, J. Math. Soc. Japan 65 (2013) 411 MR3055592
24 I Kra, On the Nielsen–Thurston–Bers type of some self-maps of Riemann surfaces, Acta Math. 146 (1981) 231 MR611385
25 E Lanneau, J L Thiffeault, On the minimum dilatation of braids on punctured discs, Geom. Dedicata 152 (2011) 165 MR2795241
26 J Malestein, A Putman, Pseudo-Anosov dilatations and the Johnson filtration, Groups Geom. Dyn. 10 (2016) 771 MR3513117
27 B Martelli, M Novaga, A Pluda, S Riolo, Spines of minimal length, Ann. Sc. Norm. Super. Pisa Cl. Sci. 17 (2017) 1067 MR3726835
28 H Minakawa, Examples of pseudo-Anosov homeomorphisms with small dilatations, J. Math. Sci. Univ. Tokyo 13 (2006) 95 MR2277516
29 J Pankau, Salem number stretch factors and totally real fields arising from Thurston’s construction, preprint (2017) arXiv:1711.06374
30 R C Penner, Bounds on least dilatations, Proc. Amer. Math. Soc. 113 (1991) 443 MR1068128
31 H Shin, B Strenner, Pseudo-Anosov mapping classes not arising from Penner’s construction, Geom. Topol. 19 (2015) 3645 MR3447112
32 W T Song, Upper and lower bounds for the minimal positive entropy of pure braids, Bull. London Math. Soc. 37 (2005) 224 MR2119022
33 W T Song, K H Ko, J E Los, Entropies of braids, J. Knot Theory Ramifications 11 (2002) 647 MR1915500
34 B Strenner, L Liechti, Minimal pseudo-Anosov stretch factors on nonorientable surfaces, preprint (2018) arXiv:1806.00033
35 O Teichmüller, Ein Verschiebungssatz der quasikonformen Abbildung, Deutsche Math. 7 (1944) 336 MR0018761
36 W P Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. 19 (1988) 417 MR956596
37 C Y Tsai, The asymptotic behavior of least pseudo-Anosov dilatations, Geom. Topol. 13 (2009) 2253 MR2507119
38 M Yazdi, Lower bound for dilatations, J. Topol. 11 (2018) 602 MR3830877