Algebraic & Geometric Topology Volume 21, issue 3 (2021)

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Limits of sequences of pseudo-Anosov maps and of hyperbolic $3$–manifolds

Sylvain Bonnot, André de Carvalho, Juan González-Meneses and Toby Hall

Algebraic & Geometric Topology 21 (2021) 1351–1370

DOI: 10.2140/agt.2021.21.1351

Bibliography

1	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
2	R Benedetti, C Petronio, Lectures on hyperbolic geometry, Springer (1992) MR1219310
3	M Bestvina, M Handel, Train-tracks for surface homeomorphisms, Topology 34 (1995) 109 MR1308491
4	J S Birman, Braids, links, and mapping class groups, 82, Princeton Univ. Press (1974) MR0375281
5	P Boyland, Topological methods in surface dynamics, Topology Appl. 58 (1994) 223 MR1288300
6	P Boyland, A de Carvalho, T Hall, Natural extensions of unimodal maps: virtual sphere homeomorphisms and prime ends of basin boundaries, Geom. Topol. 25 (2021) 111 MR4226229
7	A de Carvalho, Extensions, quotients and generalized pseudo-Anosov maps, from: "Graphs and patterns in mathematics and theoretical physics" (editors M Lyubich, L Takhtajan), Proc. Sympos. Pure Math. 73, Amer. Math. Soc. (2005) 315 MR2131019
8	A de Carvalho, T Hall, Unimodal generalized pseudo-Anosov maps, Geom. Topol. 8 (2004) 1127 MR2087080
9	A de Carvalho, T Hall, Paper folding, Riemann surfaces and convergence of pseudo-Anosov sequences, Geom. Topol. 16 (2012) 1881 MR2975296
10	A J Casson, S A Bleiler, Automorphisms of surfaces after Nielsen and Thurston, 9, Cambridge Univ. Press (1988) MR964685
11	M Culler, N M Dunfield, M Goerner, J R Weeks, SnapPy : a computer program for studying the geometry and topology of 3–manifolds
12	B Farb, C J Leininger, D Margalit, Small dilatation pseudo-Anosov homeomorphisms and 3–manifolds, Adv. Math. 228 (2011) 1466 MR2824561
13	A Fathi, F Laudenbach, V Poénaru, editors, Travaux de Thurston sur les surfaces, 66–67, Soc. Math. France (1979) 284 MR568308
14	V Gebhardt, A new approach to the conjugacy problem in Garside groups, J. Algebra 292 (2005) 282 MR2166805
15	V Gebhardt, J González-Meneses, The cyclic sliding operation in Garside groups, Math. Z. 265 (2010) 85 MR2606950
16	V Gebhardt, J González-Meneses, Solving the conjugacy problem in Garside groups by cyclic sliding, J. Symbolic Comput. 45 (2010) 629 MR2639308
17	T Hall, The creation of horseshoes, Nonlinearity 7 (1994) 861 MR1275533
18	T Hall, Trains : an implementation of the Bestvina–Handel algorithm, software (2009)
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	C T McMullen, Renormalization and 3–manifolds which fiber over the circle, 142, Princeton Univ. Press (1996) MR1401347
21	W D Neumann, D Zagier, Volumes of hyperbolic three-manifolds, Topology 24 (1985) 307 MR815482
22	J P Otal, The hyperbolization theorem for fibered 3–manifolds, 7, Amer. Math. Soc. (2001) MR1855976
23	R C Penner, Bounds on least dilatations, Proc. Amer. Math. Soc. 113 (1991) 443 MR1068128
24	D Rolfsen, Knots and links, 7, Publish or Perish (1976) MR0515288
25	S Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967) 747 MR228014
26	W P Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. 19 (1988) 417 MR956596
27	W P Thurston, Hyperbolic structures on 3–manifolds, II : Surface groups and 3–manifolds which fiber over the circle, preprint (1998) arXiv:math/9801045
28	W P Thurston, Geometry and topology of three-manifolds, lecture notes (2002)