Volume 17, issue 4 (2013)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 28
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
A variation of McShane's identity for 2–bridge links

Donghi Lee and Makoto Sakuma

Geometry & Topology 17 (2013) 2061–2101
Bibliography
1 W Abikoff, The real analytic theory of Teichmüller space, Lecture Notes in Mathematics 820, Springer (1980) MR590044
2 H Akiyoshi, H Miyachi, M Sakuma, A refinement of McShane's identity for quasifuchsian punctured torus groups, from: "In the tradition of Ahlfors and Bers, III" (editors W Abikoff, A Haas), Contemp. Math. 355, Amer. Math. Soc. (2004) 21 MR2145054
3 H Akiyoshi, H Miyachi, M Sakuma, Variations of McShane's identity for punctured surface groups, from: "Spaces of Kleinian groups" (editors Y N Minsky, M Sakuma, C Series), London Math. Soc. Lecture Note Ser. 329, Cambridge Univ. Press (2006) 151 MR2258748
4 H Akiyoshi, M Sakuma, M Wada, Y Yamashita, Punctured torus groups and 2–bridge knot groups. I, Lecture Notes in Mathematics 1909, Springer (2007) MR2330319
5 B H Bowditch, A proof of McShane's identity via Markoff triples, Bull. London Math. Soc. 28 (1996) 73 MR1356829
6 B H Bowditch, A variation of McShane's identity for once-punctured torus bundles, Topology 36 (1997) 325 MR1415591
7 B H Bowditch, Markoff triples and quasi-Fuchsian groups, Proc. London Math. Soc. 77 (1998) 697 MR1643429
8 W Dicks, M Sakuma, On hyperbolic once-punctured-torus bundles. III. Comparing two tessellations of the complex plane, Topology Appl. 157 (2010) 1873 MR2646422
9 D B A Epstein, R C Penner, Euclidean decompositions of noncompact hyperbolic manifolds, J. Differential Geom. 27 (1988) 67 MR918457
10 F Guéritaud, Géométrie hyperbolique effective et triangulations idéales canoniques en dimension trois, PhD thesis, Université Paris Sud – Paris XI (2006)
11 F Guéritaud, On canonical triangulations of once-punctured torus bundles and two-bridge link complements, Geom. Topol. 10 (2006) 1239 MR2255497
12 D Lee, M Sakuma, Simple loops on 2–bridge spheres in 2–bridge link complements, Electron. Res. Announc. Math. Sci. 18 (2011) 97 MR2832095
13 D Lee, M Sakuma, Epimorphisms between 2–bridge link groups: homotopically trivial simple loops on 2–bridge spheres, Proc. Lond. Math. Soc. 104 (2012) 359 MR2880244
14 D Lee, M Sakuma, Homotopically equivalent simple loops on 2–bridge spheres in 2–bridge link complements (I), to appear in Geom. Dedicata arXiv:1010.2232
15 D Lee, M Sakuma, Homotopically equivalent simple loops on 2–bridge spheres in 2–bridge link complements (II), to appear in Geom. Dedicata arXiv:1103.0856
16 D Lee, M Sakuma, Homotopically equivalent simple loops on 2–bridge spheres in 2–bridge link complements (III), to appear in Geom. Dedicata arXiv:1111.3562
17 K Matsuzaki, M Taniguchi, Hyperbolic manifolds and Kleinian groups, Oxford University Press (1998) MR1638795
18 G McShane, A remarkable identity for lengths of curves, PhD thesis, University of Warwick (1991)
19 G McShane, Simple geodesics and a series constant over Teichmuller space, Invent. Math. 132 (1998) 607 MR1625712
20 M Mirzakhani, Simple geodesics and Weil–Petersson volumes of moduli spaces of bordered Riemann surfaces, Invent. Math. 167 (2007) 179 MR2264808
21 T Nakanishi, A series associated to generating pairs of a once punctured torus group and a proof of McShane's identity, Hiroshima Math. J. 41 (2011) 11 MR2809045
22 T Ohtsuki, R Riley, M Sakuma, Epimorphisms between 2–bridge link groups, from: "The Zieschang Gedenkschrift" (editors M Boileau, M Scharlemann, R Weidmann), Geom. Topol. Monogr. 14 (2008) 417 MR2484712
23 M Sakuma, Variations of McShane's identity for the Riley slice and 2–bridge links, Sūrikaisekikenkyūsho Kōkyūroku 1104 (1999) 103 MR1744474
24 M Sakuma, Epimorphisms between 2–bridge knot groups from the view point of Markoff maps, from: "Intelligence of low dimensional topology 2006" (editors J S Carter, S Kamada, L H Kauffman, A Kawauchi, T Kohno), Ser. Knots Everything 40, World Sci. Publ., Hackensack, NJ (2007) 279 MR2371736
25 M Sakuma, J Weeks, Examples of canonical decompositions of hyperbolic link complements, Japan. J. Math. 21 (1995) 393 MR1364387
26 H Schubert, Knoten mit zwei Brücken, Math. Z. 65 (1956) 133 MR0082104
27 M Sheingorn, Characterization of simple closed geodesics on Fricke surfaces, Duke Math. J. 52 (1985) 535 MR792188
28 S P Tan, Y L Wong, Y Zhang, The $\mathrm{SL}(2,\mathbb C)$ character variety of a one-holed torus, Electron. Res. Announc. Amer. Math. Soc. 11 (2005) 103 MR2191691
29 S P Tan, Y L Wong, Y Zhang, Generalizations of McShane's identity to hyperbolic cone-surfaces, J. Differential Geom. 72 (2006) 73 MR2215456
30 S P Tan, Y L Wong, Y Zhang, Necessary and sufficient conditions for McShane's identity and variations, Geom. Dedicata 119 (2006) 199 MR2247658
31 S P Tan, Y L Wong, Y Zhang, End invariants for $\mathrm{SL}(2,\mathbb C)$ characters of the one-holed torus, Amer. J. Math. 130 (2008) 385 MR2405161
32 S P Tan, Y L Wong, Y Zhang, Generalized Markoff maps and McShane's identity, Adv. Math. 217 (2008) 761 MR2370281
33 S P Tan, Y L Wong, Y Zhang, McShane's identity for classical Schottky groups, Pacific J. Math. 237 (2008) 183 MR2415214
34 W P Thurston, The geometry and topology of three-manifolds, Princeton Univ. Math. Dept. Lecture Notes (1979)
35 M Wada, OPTi
36 J Weeks, SnapPea
37 J R Weeks, Convex hulls and isometries of cusped hyperbolic $3$–manifolds, Topology Appl. 52 (1993) 127 MR1241189
38 Y Yamashita, calc.py (2012)