Volume 12, issue 4 (2008)

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

Volume 23
Issue 4, 1621–2164
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540

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
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Other MSP Journals
Multiplicities of simple closed geodesics and hypersurfaces in Teichmüller space

Greg McShane and Hugo Parlier

Geometry & Topology 12 (2008) 1883–1919
Bibliography
1 W Abikoff, The real analytic theory of Teichmüller space, Lecture Notes in Math. 820, Springer (1980) MR590044
2 A Baragar, On the unicity conjecture for Markoff numbers, Canad. Math. Bull. 39 (1996) 3 MR1382484
3 A F Beardon, The geometry of discrete groups, Graduate Texts in Math. 91, Springer (1995) MR1393195
4 R Brown, Topology, Ellis Horwood Series: Math. and its Applications, Ellis Horwood Ltd. (1988) MR984598
5 P Buser, Geometry and spectra of compact Riemann surfaces, Progress in Math. 106, Birkhäuser (1992) MR1183224
6 P Buser, K D Semmler, The geometry and spectrum of the one-holed torus, Comment. Math. Helv. 63 (1988) 259 MR948781
7 J O Button, The uniqueness of the prime Markoff numbers, J. London Math. Soc. $(2)$ 58 (1998) 9 MR1666058
8 J O Button, Markoff numbers, principal ideals and continued fraction expansions, J. Number Theory 87 (2001) 77 MR1816037
9 A J Casson, S A Bleiler, Automorphisms of surfaces after Nielsen and Thurston, London Math. Soc. Student Texts 9, Cambridge University Press (1988) MR964685
10 H Cohn, Approach to Markoff's minimal forms through modular functions, Ann. of Math. $(2)$ 61 (1955) 1 MR0067935
11 H Cohn, Representation of Markoff's binary quadratic forms by geodesics on a perforated torus, Acta Arith. 18 (1971) 125 MR0288079
12 G Frobenius, Uber die Markovschen Zahlen, Preuss. Akad. Wiss. Sitzungsberichte (1913) 458
13 T Gauglhofer, K D Semmler, Trace coordinates of Teichmüller space of Riemann surfaces of signature $(0,4)$, Conform. Geom. Dyn. 9 (2005) 46 MR2133805
14 W M Goldman, The modular group action on real $\mathrm{SL}(2)$–characters of a one-holed torus, Geom. Topol. 7 (2003) 443 MR2026539
15 D Griffiths, At most 27 length inequalities define Maskit's fundamental domain for the modular group in genus 2, from: "The Epstein birthday schrift", Geom. Topol. Monogr. 1, Geom. Topol. Publ., Coventry (1998) 167 MR1668355
16 A Haas, Diophantine approximation on hyperbolic Riemann surfaces, Acta Math. 156 (1986) 33 MR822330
17 U Hamenstädt, Length functions and parameterizations of Teichmüller space for surfaces with cusps, Ann. Acad. Sci. Fenn. Math. 28 (2003) 75 MR1976831
18 S P Kerckhoff, The Nielsen realization problem, Ann. of Math. $(2)$ 117 (1983) 235 MR690845
19 M L Lang, S P Tan, A simple proof of the Markoff conjecture for prime powers, Geom. Dedicata 129 (2007) 15 MR2353978
20 B Maskit, A picture of moduli space, Invent. Math. 126 (1996) 341 MR1411137
21 G McShane, I Rivin, A norm on homology of surfaces and counting simple geodesics, Internat. Math. Res. Notices (1995) 61 MR1317643
22 M Mirzakhani, Simple geodesics and Weil–Petersson volumes of moduli spaces of bordered Riemann surfaces, submitted (2003)
23 B Randol, The length spectrum of a Riemann surface is always of unbounded multiplicity, Proc. Amer. Math. Soc. 78 (1980) 455 MR553396
24 I Rivin, Simple curves on surfaces, Geom. Dedicata 87 (2001) 345 MR1866856
25 P C Sarnak, Diophantine problems and linear groups, from: "Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990)", Math. Soc. Japan (1991) 459 MR1159234
26 T A Schmidt, M Sheingorn, Parametrizing simple closed geodesy on $\Gamma^3\backslash\mathcal H$, J. Aust. Math. Soc. 74 (2003) 43 MR1948257
27 P Schmutz, Systoles of arithmetic surfaces and the Markoff spectrum, Math. Ann. 305 (1996) 191 MR1386112
28 P Schmutz Schaller, Geometry of Riemann surfaces based on closed geodesics, Bull. Amer. Math. Soc. $($N.S.$)$ 35 (1998) 193 MR1609636
29 C Series, The geometry of Markoff numbers, Math. Intelligencer 7 (1985) 20 MR795536
30 W Thurston, Minimal stretch maps between surfaces arXiv:math.GT/9801039