Volume 17, issue 4 (2017)

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ISSN (electronic): 1472-2739
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The diagonal slice of Schottky space

Caroline Series, Ser Peow Tan and Yasushi Yamashita

Algebraic & Geometric Topology 17 (2017) 2239–2282
Bibliography
1 H Akiyoshi, M Sakuma, M Wada, Y Yamashita, Punctured torus groups and 2–bridge knot groups, I, 1909, Springer (2007) MR2330319
2 F Bonahon, J P Otal, Laminations measurées de plissage des variétés hyperboliques de dimension 3, Ann. of Math. 160 (2004) 1013 MR2144972
3 B H Bowditch, Markoff triples and quasi-Fuchsian groups, Proc. London Math. Soc. 77 (1998) 697 MR1643429
4 R D Canary, Pushing the boundary, from: "In the tradition of Ahlfors and Bers, III" (editors W Abikoff, A Haas), Contemp. Math. 355, Amer. Math. Soc. (2004) 109 MR2145059
5 Y E Choi, C Series, Lengths are coordinates for convex structures, J. Differential Geom. 73 (2006) 75 MR2217520
6 M Culler, Lifting representations to covering groups, Adv. in Math. 59 (1986) 64 MR825087
7 D B A Epstein, A Marden, Convex hulls in hyperbolic space, a theorem of Sullivan, and measured pleated surfaces, from: "Analytical and geometric aspects of hyperbolic space" (editor D B A Epstein), London Math. Soc. Lec. Note Ser. 111, Cambridge Univ. Press (1987) 113 MR903852
8 W Fenchel, Elementary geometry in hyperbolic space, 11, De Gruyter (1989) MR1004006
9 W M Goldman, The modular group action on real SL(2)–characters of a one-holed torus, Geom. Topol. 7 (2003) 443 MR2026539
10 W M Goldman, Trace coordinates on Fricke spaces of some simple hyperbolic surfaces, from: "Handbook of Teichmüller theory, Vol II" (editor A Papadopoulos), IRMA Lect. Math. Theor. Phys. 13, Eur. Math. Soc. (2009) 611 MR2497777
11 W Goldman, G McShane, G Stantchev, S P Tan, Automorphisms of two-generator free groups and spaces of isometric actions on the hyperbolic plane, preprint (2015) arXiv:1509.03790
12 J Hempel, 3–Manifolds, 86, Princeton Univ. Press (1976) MR0415619
13 C D Hodgson, S P Kerckhoff, Rigidity of hyperbolic cone-manifolds and hyperbolic Dehn surgery, J. Differential Geom. 48 (1998) 1 MR1622600
14 L Keen, C Series, Pleating coordinates for the Maskit embedding of the Teichmüller space of punctured tori, Topology 32 (1993) 719 MR1241870
15 L Keen, C Series, The Riley slice of Schottky space, Proc. London Math. Soc. 69 (1994) 72 MR1272421
16 L Keen, C Series, Continuity of convex hull boundaries, Pacific J. Math. 168 (1995) 183 MR1331998
17 L Keen, C Series, How to bend pairs of punctured tori, from: "Lipa’s legacy" (editors J Dodziuk, L Keen), Contemp. Math. 211, Amer. Math. Soc. (1997) 359 MR1476997
18 L Keen, C Series, Pleating invariants for punctured torus groups, Topology 43 (2004) 447 MR2052972
19 Y Komori, C Series, The Riley slice revisited, from: "The Epstein birthday schrift" (editors I Rivin, C Rourke, C Series), Geom. Topol. Monogr. 1, Geom. Topol. Publ. (1998) 303 MR1668296
20 I Kra, On lifting Kleinian groups to SL(2,C), from: "Differential geometry and complex analysis" (editors I Chavel, H M Farkas), Springer (1985) 181 MR780044
21 F Luo, Simple loops on surfaces and their intersection numbers, Math. Res. Lett. 5 (1998) 47 MR1618359
22 S Maloni, F Palesi, S P Tan, On the character variety of the four-holed sphere, Groups Geom. Dyn. 9 (2015) 737 MR3420542
23 A Marden, Hyperbolic manifolds : an introduction in 2 and 3 dimensions, Cambridge Univ. Press (2016)
24 B Maskit, Kleinian groups, 287, Springer (1988) MR959135
25 S P K Ng, S P Tan, The complement of the Bowditch space in the SL(2, ) character variety, Osaka J. Math. 44 (2007) 247 MR2351001
26 J P Otal, Sur le coeur convexe d’une variété hyperbolique de dimension 3, preprint (1994)
27 C Series, The geometry of Markoff numbers, Math. Intelligencer 7 (1985) 20 MR795536
28 C Series, An extension of Wolpert’s derivative formula, Pacific J. Math. 197 (2001) 223 MR1810217
29 S P Tan, Y L Wong, Y Zhang, Necessary and sufficient conditions for McShane’s identity and variations, Geom. Dedicata 119 (2006) 199 MR2247658
30 S P Tan, Y L Wong, Y Zhang, Generalized Markoff maps and McShane’s identity, Adv. Math. 217 (2008) 761 MR2370281
31 M Wada, Software OPTi
32 M Wada, OPTi’s algorithm for discreteness determination, Experiment. Math. 15 (2006) 61 MR2229386