Volume 10, issue 4 (2010)

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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