Finite covers of random 3-manifolds

Inventiones Mathematicae

Volumn 166, Issue 3, 2006, Pages 457-521

  Dunfield, Nathan M ^a   Thurston, William P ^b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b Department of Obstetrics Gynecology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33750510901     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00222-006-0001-6     Document Type: Article

References (58)

1. [AS] Alon, N., Spencer. J.H.: The Probabilistic Method, 2nd edn., Wiley-Interscience Series in Discrete Mathematics and Optimization,. New York: Wiley-Interscience 2000
2. [BL] Belolipetsky, M., Lubotzky, A.: Finite groups and hyperbolic manifolds. Invent. Math. 162, 459-472 (2005). arXiv:math.GR/0406607
3. [Bol] Bollobás, B.: Random Graphs. London: Academic Press 1985
4. [Bro] Brown, K.S.: Cohomology of Groups. Graduate Texts in Mathematics, vol. 87. New York: Springer 1982
5. [Car] Carlitz, L.: Representations by quadratic forms in a finite field. Duke Math. J. 21, 123-137 (1954)
6. [CF] Conner, P.E., Floyd. E.E.: Differentiable Periodic Maps. Ergebnisse der Mathematik und ihrer Grenzgebiete. N,F., Band 33. Berlin: Springer 1964
7. [Con] Conner, P.E.: Differentiable Periodic Maps. 2nd edn. Lect. Notes Math. vol. 738. Berlin: Springer 1979
8. [CCNPW] Conway, J.H., Curtis, R.T. Norton, S.P.. Parker, R.A., Wilson, R.A.: Atlas of Finite Groups. Eynsham: Oxford University Press 1985
9. [DSC] Diaconis, P.. Saloff-Coste, L.: Walks on generating sets of groups. Invent. Math. 134, 251-299 (1998)
10. [DPS] Diao, Y., Pippenger, N., Sumners, D.W.: On random knots. In: Random Knotting and Linking (Vancouver, BC. 1993). of Ser. Knots Everything, vol. 7. pp. 187-197. River Edge, NJ: World Sei. Publishing 1994
11. [DdSMS] Dixon, J.D., du Sautoy, M.P.E., Mann. A.. Segal. D.: Analytic pro-p Groups, 2nd edn. Cambridge Studies in Advanced Mathematics, vol. 61. Cambridge: Cambridge University Press 1999
12. [DM] Dixon, J.D., Mortimer. B.: Permutation Groups. Graduate Texts in Mathematics. vol. 163. New York: Springer 1996
13. [DT1] Dunfield, N.M.. Thurston, D.P.: A random tunnel number one 3-manifold does not fiber over the circle. Preprint, 2005. arXiv:math.GT/0510129
14. [DT2] Dunfield, N.M., Thurston, W.P.: The virtual haken conjecture: experiments and examples. Guom. Topol. 7, 399-441 (2003). arXiv:math.GT/0209214
15. [Edm] Edmonds, A.L.: Surface symmetry. II. Michigan Math. J. 30, 143-154 (1983)
16. [Eva] Evans, M.J.: TV-systems of certain finite simple groups. Math. Proc. Cambr. Philos. Soc. 113, 9-22 (1993)
17. [Eve] Everitt, B.: Alternating quotients of Fuchsian groups. J. Algebra 223, 457-476 (2000)
18. [Fel] Feller. W.: An Introduction to Probability Theory and its Applications. Vol. I, 3rd edn. New York: John Wiley & Sons Inc. 1968
19. [Gil] Gilman, R.: Finite quotients of the automorphism group of a free group. Can. J.Math. 29, 541-551 (1977)
20. [Gol] Goldman, W.M. Ergodic theory on moduli spaces. Ann. Math. 146, 475-507 (1997)
21. [Gro1] Gromov, M.: Asymptotic invariants of infinite groups. In: Geometric Group Theory, vol. 2 (Sussex, 1991), Lond. Math. Soc. Lecture Note Ser., vol. 182, pp. 1-295. Cambridge: Cambridge University Press 1993
22. Gro2] Gromov, M,: Random walk in random groups. Geom, Fund. Anal. 13, 73-146 (2003)
23. [Hal] Hall. P.: The Eulcrian functions of a group. Quart. J. Math. 7, 134-151 (1936)
24. [HZ] Harer, J., Zagier, D.: The Euler characteristic of the moduli space of curves. Invent. Math. 85, 457-485 (1986)
25. [Hem1] Hempel, J.: The lattice of branched covers over the figure-eight knot. Topology Appl. 34, 183-201 (1990)
26. [Hem2] Hempel, J.: 3-manifolds as viewed from the curve complex. Topology 40, 631-657 (2001)
27. [HLM] Hilden, H.M., Loza M.T., Montesinos, J.M.: On knots that are universal. Topology 24, 499-504 (1985)
28. [IZ] Itzykson, C., Zuber, J.-B.: Matrix integration and combinatorics of modular groups. Commun. Math. Phys. 134, 197-207 (1990)
29. [Jac] Jackson, D.M.: Counting cycles in permutations by group characters, with an application to a topological problem. Trans. Am. Math. Soc. 299, 785-801 (1987)
30. [Jun] Jungreis. D.: Gaussian random polygons are globally knotted. J. Knot Theory Ramifications 3, 455-464 (1994)
31. [LN] Ledermann, W., Neumann, B.H.: On the order of the automorphism group of a finite group, I. Proc. R. Soc. Lond., Ser. A. 233, 494-506 (1956)
32. [LS1] Liebeck, M.W., Shalev, A.: Fuchsian groups, coverings of Riemann surfaces, subgroup growth, random quotients and random walks. J. Algebra 276.552-601 (2004)
33. [LS2] Liebeck, M.W., Shalev, A.: Fuchsian groups, finite simple groups and representation varieties. Invent. Math. 159, 317-367 (2005)
34. [Liv] Livingston. C.: Stabilizing surface symmetries. Mich. Math. J. 32, 249-255 (1985)
35. [Lub1[ Lubotzky, A.: Discrete Groups. Expanding Graphs and Invariant Measures. Progress in Mathematics, vol. 125. Basel: Birkhäuser 1994
36. [Lub2] Lubotzky, A.: Subgroup growth and congruence subgroups. Invent. Math. 119, 267-295 (1995)
37. [LS] Lubotzky, A., Segal, D.: Subgroup Growth. Progress in Mathematics, vol. 212. Basel: Birkhäuser 2003
38. [Mac] MacWilliams, J.: Orthogonal matrices over finite fields. Am. Math. Monthly 76, 152-164 (1969)
39. [Mah] Maher, J. Random walks on the mapping class group. Preprint 2006. arXiv:math.GT/0604433
40. [Nam] Namazi, H.: Heegaard Splittings and Hyperbolic Geometry. PhD thesis, Yale 2005
41. [Ol] Ol'shanskiǐ. A.Y.: Almost every group is hyperbolic. Int. J. Algebra Comput. 2, 1-17 (1992)
42. [Pak] Pak, L: What do we know about the product replacement algorithm? In: Groups and Computation, III (Columbus. OH. 1999). Ohio State Univ. Math. Res. Inst. Publ., vol. 8, pp. 301-347. Berlin: de Gruyter 2001
43. [Pen] Penner. R.C.: Perturbative series and the moduli space of Riemann surfaces. J. Differ. Geom. 27, 35-53 (1988)
44. [Per1] Perelman, G.: The entropy formula for the Ricci flow and its geometric applications. Preprint 2002. arXiv:math.DG/0211159
45. [Per2] Perelman, G.: Ricci flow with surgery on three-manifolds, Preprint 2003. arXiv:math.DG/0303109
46. [PS] Poulalhon, D., Schaeffer, G.: Optimal coding and sampling of triangulations. Preprint. 2003
47. [RZ] Ribes, I., Zalesskii, P.: Profinite Groups. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge., vol. 40. Berlin: Springer 2000
48. [Sim] Sims, C.C.: Computation with Finitely Presented Groups. Cambridge: Cambridge University Press 1994
49. [Sta] Stanley, R.P.: Spanning trues and a conjecture of Kontsevich, Ann. Comb. 2, 351-363 (1998). arXiv:math.CO/9806055
50. [Wal] Waldhausen, F.: The word problem in fundamental groups of sufficiently large irreducible 3-manifolds. Ann. Math. 88, 272-280 (1968)
51. [Wei] Weisfeiler, B.: Strong approximation for Zariski-dense subgroups of semisimple algebraic groups. Ann. Math. 120, 271-315 (1984)
52. [Whi] White, M.E.: Injectivity radius and fundamental groups of hyperbolic 3-manifolds. Commun. Anal. Geom. 10, 377-395 (2002)
53. [Wie] Wiegold, T.: The Schur multiplier an elementary approach. In: Groups - St. Andrews 1981 (St. Andrews. 1981). Lond. Math. Soc. Lecture Note Ser., vol. 71, pp. 137-154. Cambridge: Cambridge University Press 1982
54. [Wil] Wilson, J.S.: Profinite Groups. Lond. Math. Soc. Monographs. New Series, vol. 19. New York: The Clarendon Press Oxford University Press 1998
55. [Wor] Wormald. N.C.: Models of random regular graphs. In: Surveys in Combinatorics, 1999 (Canterbury). Lond. Math. Soc. Lecture Note Ser., vol. 267, pp. 239-298. Cambridge: Cambridge University Press 1999
56. [Zag] Zagier, D.: On the distribution of the number of cycles of elements in symmetric groups. Nieuw Arch. Wiskd. 13, 489-495 (1995)
57. [Zim] Zimmermann. B.: Surfaces and the second homo logy of a group. Monatsh. Math. 104, 247-253 (1987)
58. [Zuk] Żuk, A.: Property (T) and Kazhdan constants for discrete groups. Geom. Funct. Anal. 13, 643-670 (2003)