Volume 10, issue 1 (2006)

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
Automorphic forms and rational homology 3–spheres

Frank Calegari and Nathan M Dunfield

Geometry & Topology 10 (2006) 295–329
Bibliography
1 M Baker, M Boileau, S Wang, Towers of covers of hyperbolic 3–manifolds, Rend. Istit. Mat. Univ. Trieste 32 (2001) MR1893391
2 N Boston, J S Ellenberg, Pro–p groups and towers of rational homology spheres, Geom. Topol. 10 (2006) 331
3 A Brumer, K Kramer, Non-existence of certain semistable abelian varieties, Manuscripta Math. 106 (2001) 291 MR1869222
4 F Calegari, Semistable abelian varieties over , Manuscripta Math. 113 (2004) 507 MR2129874
5 F Calegari, N M Dunfield, Data files and Magma programs
6 H Carayol, Sur les représentations l–adiques associées aux formes modulaires de Hilbert, Ann. Sci. École Norm. Sup. (4) 19 (1986) 409 MR870690
7 L Clozel, On the cuspidal cohomology of arithmetic subgroups of SL(2n) and the first Betti number of arithmetic 3–manifolds, Duke Math. J. 55 (1987) 475 MR894591
8 L Clozel, On the cohomology of Kottwitz’s arithmetic varieties, Duke Math. J. 72 (1993) 757 MR1253624
9 C A Group, Magma, version 2.12 (2003)
10 D Coulson, O A Goodman, C D Hodgson, W D Neumann, Computing arithmetic invariants of 3–manifolds, Experiment. Math. 9 (2000) 127 MR1758805
11 J E Cremona, Hyperbolic tessellations, modular symbols, and elliptic curves over complex quadratic fields, Compositio Math. 51 (1984) 275 MR743014
12 J D Dixon, M P F du Sautoy, A Mann, D Segal, Analytic pro-p groups, 61, Cambridge University Press (1999) MR1720368
13 N M Dunfield, W P Thurston, The virtual Haken conjecture : experiments and examples, Geom. Topol. 7 (2003) 399 MR1988291
14 J M Fontaine, Il n’y a pas de variété abélienne sur , Invent. Math. 81 (1985) 515 MR807070
15 O Goodman, Snap : a computer program for studying arithmetic invariants of hyperbolic 3–manifolds
16 F Grunewald, H Helling, J Mennicke, SL2 over complex quadratic number fields I, Algebra i Logika 17 (1978) 512, 622 MR555260
17 G Harder, Eisenstein cohomology of arithmetic groups. The case GL2, Invent. Math. 89 (1987) 37 MR892187
18 M Harris, D Soudry, R Taylor, l–adic representations associated to modular forms over imaginary quadratic fields I : Lifting to GSp4(), Invent. Math. 112 (1993) 377 MR1213108
19 D Heard, Orb: a program for computing hyperbolic structures on orbifolds
20 H M Hilden, M T Lozano, J M Montesinos-Amilibia, On the arithmetic 2–bridge knots and link orbifolds and a new knot invariant, J. Knot Theory Ramifications 4 (1995) 81 MR1321291
21 J Hoste, P D Shanahan, Commensurability classes of twist knots, J. Knot Theory Ramifications 14 (2005) 91 MR2124555
22 H Jacquet, R P Langlands, Automorphic forms on GL(2), Springer (1970) MR0401654
23 R C Kirby, Problems in low-dimensional topology, from: "Geometric topology (Athens, GA, 1993)", AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 35 MR1470751
24 J P Labesse, J Schwermer, On liftings and cusp cohomology of arithmetic groups, Invent. Math. 83 (1986) 383 MR818358
25 A Lubotzky, Group presentation, p–adic analytic groups and lattices in SL2(), Ann. of Math. (2) 118 (1983) 115 MR707163
26 A Lubotzky, Eigenvalues of the Laplacian, the first Betti number and the congruence subgroup problem, Ann. of Math. (2) 144 (1996) 441 MR1418904
27 A Lubotzky, Free quotients and the first Betti number of some hyperbolic manifolds, Transform. Groups 1 (1996) 71 MR1390750
28 C Maclachlan, A W Reid, The arithmetic of hyperbolic 3–manifolds, 219, Springer (2003) MR1937957
29 J Martinet, Petits discriminants des corps de nombres, from: "Number theory days, 1980 (Exeter, 1980)", London Math. Soc. Lecture Note Ser. 56, Cambridge Univ. Press (1982) 151 MR697261
30 J J Millson, On the first Betti number of a constant negatively curved manifold, Ann. of Math. (2) 104 (1976) 235 MR0422501
31 M F Newman, E A O’Brien, Application of computers to questions like those of Burnside II, Internat. J. Algebra Comput. 6 (1996) 593 MR1419133
32 G Perelman, The entropy formula for the Ricci flow and its geometric applications, arXiv:math.DG/0211159
33 G Perelman, Ricci flow with surgery on three-manifolds, arXiv:math.DG/0303109
34 C S Rajan, On the non-vanishing of the first Betti number of hyperbolic three manifolds, Math. Ann. 330 (2004) 323 MR2089429
35 M Rapoport, T Zink, Über die lokale Zetafunktion von Shimuravarietäten. Monodromiefiltration und verschwindende Zyklen in ungleicher Charakteristik, Invent. Math. 68 (1982) 21 MR666636
36 J D Rogawski, Automorphic representations of unitary groups in three variables, 123, Princeton University Press (1990) MR1081540
37 R Schoof, Abelian varieties over cyclotomic fields with good reduction everywhere, Math. Ann. 325 (2003) 413 MR1968602
38 H P F Swinnerton-Dyer, On l–adic representations and congruences for coefficients of modular forms II, from: "Modular functions of one variable, V (Proc. Second Internat. Conf., Univ. Bonn, Bonn, 1976)", Springer (1977) MR0498392
39 J Tate, The non-existence of certain Galois extensions of unramified outside 2, from: "Arithmetic geometry (Tempe, AZ, 1993)", Contemp. Math. 174, Amer. Math. Soc. (1994) 153 MR1299740
40 R Taylor, l–adic representations associated to modular forms over imaginary quadratic fields II, Invent. Math. 116 (1994) 619 MR1253207
41 R Taylor, On Galois representations associated to Hilbert modular forms II, from: "Elliptic curves, modular forms & Fermatś last theorem (Hong Kong 1993)", Ser. Number Theory I, International Press (1995) 185
42 R Taylor, A Wiles, Ring-theoretic properties of certain Hecke algebras, Ann. of Math. (2) 141 (1995) 553 MR1333036
43 R Taylor, T Yoshida, Compatibility of local and global Langlands correspondences, preprint (2004)
44 T G Group, GAP – Groups, Algorithms and Programming, version 4.2 (2000)
45 M F Vignéras, Arithmétique des algèbres de quaternions, 800, Springer (1980) MR580949
46 F Waldhausen, The word problem in fundamental groups of sufficiently large irreducible 3–manifolds, Ann. of Math. (2) 88 (1968) 272 MR0240822
47 J R Weeks, SnapPea : a computer program for investigating hyperbolic 3–manifolds
48 A Weil, On discrete subgroups of Lie groups, Ann. of Math. (2) 72 (1960) 369 MR0137792
49 A Wiles, Modular elliptic curves and Fermat’s last theorem, Ann. of Math. (2) 141 (1995) 443 MR1333035