Algebraic & Geometric Topology Volume 13, issue 6 (2013)

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Minimal dilatations of pseudo-Anosovs generated by the magic $3$–manifold and their asymptotic behavior

Eiko Kin, Sadayoshi Kojima and Mitsuhiko Takasawa

Algebraic & Geometric Topology 13 (2013) 3537–3602

DOI: 10.2140/agt.2013.13.3537

Bibliography

1	J W Aaber, N Dunfield, Closed surface bundles of least volume, Algebr. Geom. Topol. 10 (2010) 2315 MR2745673
2	I Agol, The minimal volume orientable hyperbolic $2$–cusped $3$–manifolds, Proc. Amer. Math. Soc. 138 (2010) 3723 MR2661571
3	I Agol, Ideal triangulations of pseudo-Anosov mapping tori, from: "Topology and geometry in dimension three" (editors W Li, L Bartolini, J Johnson, F Luo, R Myers, J H Rubinstein), Contemp. Math. 560, Amer. Math. Soc. (2011) 1 MR2866919
4	J O Button, Fibred and virtually fibred hyperbolic $3$–manifolds in the censuses, Experiment. Math. 14 (2005) 231 MR2169525
5	J H Cho, J Y Ham, The minimal dilatation of a genus-two surface, Experiment. Math. 17 (2008) 257 MR2455699
6	M Culler, N M Dunfield, J R Weeks, SnapPy, a computer program for studying the geometry and topology of $3$–manifolds
7	N M Dunfield, Which cusped census manifolds fiber?
8	B Farb, C J Leininger, D Margalit, Small dilatation pseudo-Anosov homeomorphisms and $3$–manifolds, Adv. Math. 228 (2011) 1466 MR2824561
9	A Fathi, F Laudenbach, V Poenaru, Travaux de Thurston sur les surfaces, Astérisque 66, Société Mathématique de 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 Gabai, R Meyerhoff, P Milley, Minimum volume cusped hyperbolic three-manifolds, J. Amer. Math. Soc. 22 (2009) 1157 MR2525782
12	J Y Ham, W T Song, The minimum dilatation of pseudo-Anosov $5$–braids, Experiment. Math. 16 (2007) 167 MR2339273
13	M Handel, The forcing partial order on the three times punctured disk, Ergodic Theory Dynam. Systems 17 (1997) 593 MR1452182
14	E Hironaka, Small dilatation mapping classes coming from the simplest hyperbolic braid, Algebr. Geom. Topol. 10 (2010) 2041 MR2728483
15	E Hironaka, E Kin, A family of pseudo-Anosov braids with small dilatation, Algebr. Geom. Topol. 6 (2006) 699 MR2240913
16	N V Ivanov, Coefficients of expansion of pseudo-Anosov homeomorphisms, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 167 (1988) 111, 191 MR964259
17	E Kin, S Kojima, M Takasawa, Entropy versus volume for pseudo-Anosovs, Experiment. Math. 18 (2009) 397 MR2583541
18	E Kin, M Takasawa, Pseudo-Anosov braids with small entropy and the magic $3$–manifold, Comm. Anal. Geom. 19 (2011) 705 MR2880213
19	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
20	E Lanneau, J L Thiffeault, On the minimum dilatation of braids on punctured discs, Geom. Dedicata 152 (2011) 165 MR2795241
21	E Lanneau, J L Thiffeault, On the minimum dilatation of pseudo-Anosov homeromorphisms on surfaces of small genus, Ann. Inst. Fourier (Grenoble) 61 (2011) 105 MR2828128
22	C J Leininger, On groups generated by two positive multi-twists: Teichmüller curves and Lehmer's number, Geom. Topol. 8 (2004) 1301 MR2119298
23	B Martelli, C Petronio, Dehn filling of the “magic” $3$–manifold, Comm. Anal. Geom. 14 (2006) 969 MR2287152
24	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
25	T Matsuoka, Braids of periodic points and a $2$–dimensional analogue of Sharkovskiĭ's ordering, from: "Dynamical systems and nonlinear oscillations" (editor G Ikegami), World Sci. Adv. Ser. Dynam. Systems 1, World Sci. Publishing (1986) 58 MR854304
26	C T McMullen, Polynomial invariants for fibered $3$–manifolds and Teichmüller geodesics for foliations, Ann. Sci. École Norm. Sup. 33 (2000) 519 MR1832823
27	H Minakawa, Examples of pseudo-Anosov homeomorphisms with small dilatations, J. Math. Sci. Univ. Tokyo 13 (2006) 95 MR2277516
28	R C Penner, Bounds on least dilatations, Proc. Amer. Math. Soc. 113 (1991) 443 MR1068128
29	W T Song, K H Ko, J E Los, Entropies of braids, J. Knot Theory Ramifications 11 (2002) 647 MR1915500
30	W P Thurston, Hyperbolic structures on $3$–manifolds II: Surface groups and $3$–manifolds which fiber over the circle arXiv:math/9801045
31	W P Thurston, A norm for the homology of $3$–manifolds, Mem. Amer. Math. Soc. 59 (1986) 99 MR823443
32	C Y Tsai, The asymptotic behavior of least pseudo-Anosov dilatations, Geom. Topol. 13 (2009) 2253 MR2507119
33	C Y Tsai, Minimal pseudo-Anosov translation lengths on the Teichmuller space, PhD thesis, University of Illinois (2010) MR2941648
34	R W Venzke, Braid forcing, hyperbolic geometry, and pseudo-Anosov sequences of low entropy, PhD thesis, California Institute of Technology (2008) MR3078552
35	A Y Zhirov, On the minimum dilation of pseudo-Anosov diffeomorphisms of a double torus, Uspekhi Mat. Nauk 50 (1995) 197 MR1331364