Geometry & Topology Volume 12, issue 4 (2008)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Multiplicities of simple closed geodesics and hypersurfaces in Teichmüller space

Greg McShane and Hugo Parlier

Geometry & Topology 12 (2008) 1883–1919

DOI: 10.2140/gt.2008.12.1883

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