Geometry & Topology Volume 19, issue 6 (2015)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Pseudo-Anosov mapping classes not arising from Penner's construction

Hyunshik Shin and Balázs Strenner

Geometry & Topology 19 (2015) 3645–3656

DOI: 10.2140/gt.2015.19.3645

Bibliography

1	P Arnoux, J C Yoccoz, Construction de difféomorphismes pseudo-Anosov, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981) 75 MR610152
2	M Bauer, An upper bound for the least dilatation, Trans. Amer. Math. Soc. 330 (1992) 361 MR1094556
3	M Bestvina, M Handel, Train tracks and automorphisms of free groups, Ann. of Math. 135 (1992) 1 MR1147956
4	A J Casson, S A Bleiler, Automorphisms of surfaces after Nielsen and Thurston, London Math. Soc. Student Texts 9, Cambridge Univ. Press (1988) MR964685
5	B Farb, D Margalit, A primer on mapping class groups, Princeton Mathematical Series 49, Princeton Univ. Press (2012) MR2850125
6	A Fathi, F Laudenbach, V Poenaru, editors, Travaux de Thurston sur les surfaces, Astérisque 66, Soc. Math. France (1979) 284 MR568308
7	E Hironaka, Small dilatation mapping classes coming from the simplest hyperbolic braid, Algebr. Geom. Topol. 10 (2010) 2041 MR2728483
8	I Kra, On the Nielsen–Thurston–Bers type of some self-maps of Riemann surfaces, Acta Math. 146 (1981) 231 MR611385
9	E Lanneau, J L Thiffeault, On the minimum dilatation of braids on punctured discs, Geom. Dedicata 152 (2011) 165 MR2795241
10	E Lanneau, J L Thiffeault, On the minimum dilatation of pseudo-Anosov homeromorphisms [sic] on surfaces of small genus, Ann. Inst. Fourier (Grenoble) 61 (2011) 105 MR2828128
11	C J Leininger, On groups generated by two positive multi-twists: Teichmüller curves and Lehmer's number, Geom. Topol. 8 (2004) 1301 MR2119298
12	D D Long, Constructing pseudo-Anosov maps, from: "Knot theory and manifolds" (editor D Rolfsen), Lecture Notes in Math. 1144, Springer (1985) 108 MR823284
13	R C Penner, A construction of pseudo-Anosov homeomorphisms, Trans. Amer. Math. Soc. 310 (1988) 179 MR930079
14	R C Penner, Bounds on least dilatations, Proc. Amer. Math. Soc. 113 (1991) 443 MR1068128
15	R C Penner, Probing mapping class groups using arcs, from: "Problems on mapping class groups and related topics" (editor B Farb), Proc. Sympos. Pure Math. 74, Amer. Math. Soc. (2006) 97 MR2264535
16	H Shin, Algebraic degrees of stretch factors in mapping class groups, preprint (2015) arXiv:1401.1836v2
17	B Strenner, Algebraic degrees and Galois conjugates of pseudo-Anosov stretch factors, preprint (2015) arXiv:1506.06412
18	W P Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. 19 (1988) 417 MR956596
19	A Y Zhirov, On the minimum dilation of pseudo-Anosov diffeomorphisms of a double torus, Uspekhi Mat. Nauk 50 (1995) 197 MR1331364