Geometry & Topology Volume 10, issue 1 (2006)

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

Automorphic forms and rational homology 3–spheres

Frank Calegari and Nathan M Dunfield

Geometry & Topology 10 (2006) 295–329

DOI: 10.2140/gt.2006.10.295

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 ℚ, 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 ℤ, 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(ℚ), 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(ℂ), 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 ℚ 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