Volume 8, issue 3 (2004)

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 (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
On groups generated by two positive multi-twists: Teichmueller curves and Lehmer's number

Christopher J Leininger

Geometry & Topology 8 (2004) 1301–1359
Bibliography
1 N A’Campo, Le groupe de monodromie du déploiement des singularités isolées de courbes planes I, Math. Ann. 213 (1975) 1 MR0377108
2 N A’Campo, Sur les valeurs propres de la transformation de Coxeter, Invent. Math. 33 (1976) 61 MR0424967
3 N A’Campo, Generic immersions of curves, knots, monodromy and Gordian number, Inst. Hautes Études Sci. Publ. Math. (1998) MR1733329
4 N A’Campo, Planar trees, slalom curves and hyperbolic knots, Inst. Hautes Études Sci. Publ. Math. (1998) MR1733330
5 M Bauer, An upper bound for the least dilatation, Trans. Amer. Math. Soc. 330 (1992) 361 MR1094556
6 A F Beardon, The geometry of discrete groups, Graduate Texts in Mathematics 91, Springer (1983) MR698777
7 S Berman, Y S Lee, R V Moody, The spectrum of a Coxeter transformation, affine Coxeter transformations, and the defect map, J. Algebra 121 (1989) 339 MR992769
8 J S Birman, Braids, links, and mapping class groups, Annals of Mathematics Studies 82, Princeton University Press (1974) MR0375281
9 J Birman, Mapping class groups, Notes from a Columbia University course (2002)
10 D W Boyd, Small Salem numbers, Duke Math. J. 44 (1977) 315 MR0453692
11 D W Boyd, Pisot and Salem numbers in intervals of the real line, Math. Comp. 32 (1978) 1244 MR0491587
12 A E Brouwer, A Neumaier, The graphs with spectral radius between 2 and $\sqrt{2+\sqrt{5}}$, Linear Algebra Appl. 114/115 (1989) 273 MR986880
13 K Calta, Veech surfaces and complete periodicity in genus two, J. Amer. Math. Soc. 17 (2004) 871 MR2083470
14 J Crisp, L Paris, The solution to a conjecture of Tits on the subgroup generated by the squares of the generators of an Artin group, Invent. Math. 145 (2001) 19 MR1839284
15 D Cvetković, M Doob, I Gutman, On graphs whose spectral radius does not exceed $(2+\sqrt{5})^{1/2}$, Ars Combin. 14 (1982) 225 MR683990
16 D Cvetković, P Rowlinson, The largest eigenvalue of a graph: a survey, Linear and Multilinear Algebra 28 (1990) 3 MR1077731
17 C J Earle, F P Gardiner, Teichmüller disks and Veech's $\mathcal{F}$–structures, from: "Extremal Riemann surfaces (San Francisco, CA, 1995)", Contemp. Math. 201, Amer. Math. Soc. (1997) 165 MR1429199
18 , Travaux de Thurston sur les surfaces, Astérisque 66, Société Mathématique de France (1979) 284 MR568308
19 V Flammang, M Grandcolas, G Rhin, Small Salem numbers, from: "Number theory in progress, Vol. 1 (Zakopane–Kościelisko, 1997)", de Gruyter (1999) 165 MR1689505
20 D Gabai, The Murasugi sum is a natural geometric operation II, from: "Combinatorial methods in topology and algebraic geometry (Rochester, N.Y., 1982)", Contemp. Math. 44, Amer. Math. Soc. (1985) 93 MR813105
21 D Gabai, Detecting fibred links in $S^3$, Comment. Math. Helv. 61 (1986) 519 MR870705
22 F R Gantmacher, The theory of matrices, Chelsea Publishing Co. (1959) MR0107649
23 F P Gardiner, N Lakic, Quasiconformal Teichmüller theory, Mathematical Surveys and Monographs 76, American Mathematical Society (2000) MR1730906
24 E Ghate, E Hironaka, The arithmetic and geometry of Salem numbers, Bull. Amer. Math. Soc. $($N.S.$)$ 38 (2001) 293 MR1824892
25 E Gutkin, C Judge, Affine mappings of translation surfaces: geometry and arithmetic, Duke Math. J. 103 (2000) 191 MR1760625
26 H Hamidi-Tehrani, Groups generated by positive multi-twists and the fake lantern problem, Algebr. Geom. Topol. 2 (2002) 1155 MR1943336
27 W J Harvey, On certain families of compact Riemann surfaces, from: "Mapping class groups and moduli spaces of Riemann surfaces (Göttingen, 1991/Seattle, WA, 1991)", Contemp. Math. 150, Amer. Math. Soc. (1993) 137 MR1234263
28 E Hironaka, Chord diagrams and Coxeter links, J. London Math. Soc. $(2)$ 69 (2004) 243 MR2025339
29 R B Howlett, Coxeter groups and $M$–matrices, Bull. London Math. Soc. 14 (1982) 137 MR647197
30 J E Humphreys, Reflection groups and Coxeter groups, Cambridge Studies in Advanced Mathematics 29, Cambridge University Press (1990) MR1066460
31 N V Ivanov, Subgroups of Teichmüller modular groups, Translations of Mathematical Monographs 115, American Mathematical Society (1992) MR1195787
32 R Kenyon, J Smillie, Billiards on rational-angled triangles, Comment. Math. Helv. 75 (2000) 65 MR1760496
33 S Kerckhoff, H Masur, J Smillie, Ergodicity of billiard flows and quadratic differentials, Ann. of Math. $(2)$ 124 (1986) 293 MR855297
34 I Kra, On the Nielsen–Thurston–Bers type of some self-maps of Riemann surfaces, Acta Math. 146 (1981) 231 MR611385
35 D H Lehmer, Factorization of certain cyclotomic functions, Ann. of Math. $(2)$ 34 (1933) 461 MR1503118
36 D D Long, Constructing pseudo–Anosov maps, from: "Knot theory and manifolds (Vancouver, B.C., 1983)", Lecture Notes in Math. 1144, Springer (1985) 108 MR823284
37 C Maclachlan, A W Reid, The arithmetic of hyperbolic 3–manifolds, Graduate Texts in Mathematics 219, Springer (2003) MR1937957
38 W Magnus, A Karrass, D Solitar, Combinatorial group theory, Dover Publications (1976) MR0422434
39 D Margalit, A lantern lemma, Algebr. Geom. Topol. 2 (2002) 1179 MR1943337
40 H Masur, Transitivity properties of the horocyclic and geodesic flows on moduli space, J. Analyse Math. 39 (1981) 1 MR632453
41 H Masur, S Tabachnikov, Rational billiards and flat structures, from: "Handbook of dynamical systems, Vol. 1A", North-Holland (2002) 1015 MR1928530
42 C T McMullen, Polynomial invariants for fibered 3–manifolds and Teichmüller geodesics for foliations, Ann. Sci. École Norm. Sup. $(4)$ 33 (2000) 519 MR1832823
43 C T McMullen, Coxeter groups, Salem numbers and the Hilbert metric, Publ. Math. Inst. Hautes Études Sci. (2002) 151 MR1953192
44 C T McMullen, Billiards and Teichmüller curves on Hilbert modular surfaces, J. Amer. Math. Soc. 16 (2003) 857 MR1992827
45 M J Mossinghoff, Polynomials with small Mahler measure, Math. Comp. 67 (1998) 1697 MR1604391
46 W D Neumann, A W Reid, Arithmetic of hyperbolic manifolds, from: "Topology '90 (Columbus, OH, 1990)", Ohio State Univ. Math. Res. Inst. Publ. 1, de Gruyter (1992) 273 MR1184416
47 R C Penner, A construction of pseudo–Anosov homeomorphisms, Trans. Amer. Math. Soc. 310 (1988) 179 MR930079
48 R C Penner, Bounds on least dilatations, Proc. Amer. Math. Soc. 113 (1991) 443 MR1068128
49 B Perron, J P Vannier, Groupe de monodromie géométrique des singularités simples, C. R. Acad. Sci. Paris Sér. I Math. 315 (1992) 1067 MR1191491
50 J C Puchta, On triangular billiards, Comment. Math. Helv. 76 (2001) 501 MR1854695
51 J G Ratcliffe, Foundations of hyperbolic manifolds, Graduate Texts in Mathematics 149, Springer (1994) MR1299730
52 D Rolfsen, Knots and links, Mathematics Lecture Series 7, Publish or Perish (1990) MR1277811
53 J H Smith, Some properties of the spectrum of a graph, from: "Combinatorial Structures and their Applications (Proc. Calgary Internat. Conf., Calgary, Alta., 1969)", Gordon and Breach (1970) 403 MR0266799
54 W P Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. $($N.S.$)$ 19 (1988) 417 MR956596
55 W P Thurston, The geometry and topology of three-manifolds, Princeton University course notes (1980)
56 W A Veech, Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards, Invent. Math. 97 (1989) 553 MR1005006
57 W A Veech, The billiard in a regular polygon, Geom. Funct. Anal. 2 (1992) 341 MR1177316
58 Y B Vorobets, Plane structures and billiards in rational polygons: the Veech alternative, Uspekhi Mat. Nauk 51 (1996) 3 MR1436653
59 B Wajnryb, A simple presentation for the mapping class group of an orientable surface, Israel J. Math. 45 (1983) 157 MR719117
60 B Wajnryb, Artin groups and geometric monodromy, Invent. Math. 138 (1999) 563 MR1719815
61 A N Zemljakov, A B Katok, Topological transitivity of billiards in polygons, Mat. Zametki 18 (1975) 291 MR0399423