Volume 10, issue 4 (2010)

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

Volume 22
Issue 5, 2007–2532
Issue 4, 1497–2006
Issue 3, 991–1495
Issue 2, 473–990
Issue 1, 1–472

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
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Small dilatation mapping classes coming from the simplest hyperbolic braid

Eriko Hironaka

Algebraic & Geometric Topology 10 (2010) 2041–2060
Bibliography
1 J Aaber, N Dunfield, Closed surface bundles of least volume, preprint (2010)
2 P Arnoux, J C Yoccoz, Construction de difféomorphismes pseudo–Anosov, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981) 75 MR610152
3 A J Casson, S A Bleiler, Automorphisms of surfaces after Nielsen and Thurston, London Mathematical Society Student Texts 9, Cambridge University Press (1988) MR964685
4 J H Cho, J Y Ham, The minimal dilatation of a genus-two surface, Experiment. Math. 17 (2008) 257 MR2455699
5 B Farb, Some problems on mapping class groups and moduli space, from: "Problems on mapping class groups and related topics", Proc. Sympos. Pure Math. 74, Amer. Math. Soc. (2006) 11 MR2264130
6 B Farb, C Leininger, D Margalit, Small dilatation pseudo-Anosovs and 3–manifolds, preprint (2009)
7 A Fathi, F Laudenbach, V Poenaru, Travaux de Thurston sur les surfaces, Astérisque 66, Société Mathématique de France (1979) 284 MR568308
8 D Fried, Flow equivalence, hyperbolic systems and a new zeta function for flows, Comment. Math. Helv. 57 (1982) 237 MR684116
9 E Hironaka, The Lehmer polynomial and pretzel links, Canad. Math. Bull. 44 (2001) 440 MR1863636
10 E Hironaka, Chord diagrams and Coxeter links, J. London Math. Soc. $(2)$ 69 (2004) 243 MR2025339
11 E Hironaka, E Kin, A family of pseudo–Anosov braids with small dilatation, Algebr. Geom. Topol. 6 (2006) 699 MR2240913
12 N V Ivanov, Coefficients of expansion of pseudo–Anosov homeomorphisms, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 167 (1988) 111, 191 MR964259
13 E Kin, M Takasawa, An asymptotic behavior of the dilatation for a family of pseudo–Anosov braids, Kodai Math. J. 31 (2008) 92 MR2414236
14 E Kin, M Takasawa, Pseudo-Anosovs on closed surfaces having small entropy and the Whitehead sister link exterior, preprint (2010)
15 T Koberda, A Silberstein, Representations of Galois groups on the homology of surfaces, preprint (2009)
16 E Lanneau, J L Thiffeault, On the minimum dilatation of pseudo–Anosov homeomorphisms on surfaces of small genus, Ann. Inst. Fourier (to appear)
17 D H Lehmer, Factorization of certain cyclotomic functions, Ann. of Math. $(2)$ 34 (1933) 461 MR1503118
18 C J Leininger, On groups generated by two positive multi-twists: Teichmüller curves and Lehmer's number, Geom. Topol. 8 (2004) 1301 MR2119298
19 B Martelli, C Petronio, Dehn filling of the “magic” 3–manifold, Comm. Anal. Geom. 14 (2006) 969 MR2287152
20 C T McMullen, Polynomial invariants for fibered 3–manifolds and Teichmüller geodesics for foliations, Ann. Sci. École Norm. Sup. $(4)$ 33 (2000) 519 MR1832823
21 C T McMullen, The Alexander polynomial of a 3–manifold and the Thurston norm on cohomology, Ann. Sci. École Norm. Sup. $(4)$ 35 (2002) 153 MR1914929
22 H Minakawa, Examples of pseudo–Anosov homeomorphisms with small dilatations, J. Math. Sci. Univ. Tokyo 13 (2006) 95 MR2277516
23 R C Penner, Bounds on least dilatations, Proc. Amer. Math. Soc. 113 (1991) 443 MR1068128
24 D Rolfsen, Knots and links, Mathematics Lecture Series 7, Publish or Perish (1976) MR0515288
25 W P Thurston, A norm for the homology of 3–manifolds, Mem. Amer. Math. Soc. 59 (1986) MR823443
26 W P Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. $($N.S.$)$ 19 (1988) 417 MR956596
27 A Y Zhirov, On the minimum dilation of pseudo–Anosov diffeomorphisms of a double torus, Uspekhi Mat. Nauk 50 (1995) 197 MR1331364