Algebraic & Geometric Topology Volume 18, issue 3 (2018)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Macfarlane hyperbolic $3$–manifolds

Joseph A Quinn

Algebraic & Geometric Topology 18 (2018) 1603–1632

DOI: 10.2140/agt.2018.18.1603

Bibliography

1	I Agol, Systoles of hyperbolic 4-manifolds, preprint (2006) arXiv:math/0612290
2	I Agol, The virtual Haken conjecture, Doc. Math. 18 (2013) 1045 MR3104553
3	M D Baker, A W Reid, Arithmetic knots in closed 3–manifolds, J. Knot Theory Ramifications 11 (2002) 903 MR1936242
4	L Bianchi, Sui gruppi di sostituzioni lineari con coefficienti appartenenti a corpi quadratici immaginarî, Math. Ann. 40 (1892) 332 MR1510727
5	F Bonahon, Low-dimensional geometry: from Euclidean surfaces to hyperbolic knots, 49, Amer. Math. Soc. (2009) MR2522946
6	A Borel, Harish-Chandra, Arithmetic subgroups of algebraic groups, Ann. of Math. 75 (1962) 485 MR0147566
7	E Chesebro, J DeBlois, Algebraic invariants, mutation, and commensurability of link complements, Pacific J. Math. 267 (2014) 341 MR3207588
8	C Corrales, E Jespers, G Leal, A del Río, Presentations of the unit group of an order in a non-split quaternion algebra, Adv. Math. 186 (2004) 498 MR2073916
9	D B A Epstein, R C Penner, Euclidean decompositions of noncompact hyperbolic manifolds, J. Differential Geom. 27 (1988) 67 MR918457
10	M Gromov, I Piatetski-Shapiro, Nonarithmetic groups in Lobachevsky spaces, Inst. Hautes Études Sci. Publ. Math. 66 (1988) 93 MR932135
11	F J Grunewald, J Schwermer, Arithmetic quotients of hyperbolic 3–space, cusp forms and link complements, Duke Math. J. 48 (1981) 351 MR620254
12	A Hatcher, Hyperbolic structures of arithmetic type on some link complements, J. London Math. Soc. 27 (1983) 345 MR692540
13	A Hurwitz, Grundlagen einer independenten Theorie der elliptischen Modulfunctionen und Theorie der Multiplicatorgleichungen erster Stufe, Diss. Leipzig, Klein Ann. 18 (1881) 528
14	M A Knus, A Merkurjev, M Rost, J P Tignol, The book of involutions, 44, Amer. Math. Soc. (1998) MR1632779
15	A Macfarlane, Hyperbolic Quaternions, Proc. Roy. Soc. Edinburgh 23 (1902) 169
16	C Maclachlan, A W Reid, Commensurability classes of arithmetic Kleinian groups and their Fuchsian subgroups, Math. Proc. Cambridge Philos. Soc. 102 (1987) 251 MR898145
17	C Maclachlan, A W Reid, The arithmetic of hyperbolic 3–manifolds, 219, Springer (2003) MR1937957
18	J Manning, Algorithmic detection and description of hyperbolic structures on closed 3–manifolds with solvable word problem, Geom. Topol. 6 (2002) 1 MR1885587
19	W D Neumann, Realizing arithmetic invariants of hyperbolic 3–manifolds, from: "Interactions between hyperbolic geometry, quantum topology and number theory" (editors A Champanerkar, O Dasbach, E Kalfagianni, I Kofman, W Neumann, N Stoltzfus), Contemp. Math. 541, Amer. Math. Soc. (2011) 233 MR2796636
20	W D Neumann, A W Reid, Arithmetic of hyperbolic manifolds, from: "Topology ’90" (editors B Apanasov, W D Neumann, A W Reid, L Siebenmann), Ohio State Univ. Math. Res. Inst. Publ. 1, de Gruyter (1992) 273 MR1184416
21	A Page, Computing arithmetic Kleinian groups, Math. Comp. 84 (2015) 2361 MR3356030
22	J A Quinn, A complex quaternion model for hyperbolic 3–space, preprint (2017) arXiv:1701.06709
23	J G Ratcliffe, Foundations of hyperbolic manifolds, 149, Springer (1994) MR1299730
24	A W Reid, A note on trace-fields of Kleinian groups, Bull. London Math. Soc. 22 (1990) 349 MR1058310
25	R Riley, Applications of a computer implementation of Poincaré’s theorem on fundamental polyhedra, Math. Comp. 40 (1983) 607 MR689477
26	R G Swan, Generators and relations for certain special linear groups, Advances in Math. 6 (1971) 1 MR0284516
27	K Takeuchi, On some discrete subgroups of SL₂(R), J. Fac. Sci. Univ. Tokyo Sect. I 16 (1969) 97 MR0262171
28	K Takeuchi, A characterization of arithmetic Fuchsian groups, J. Math. Soc. Japan 27 (1975) 600 MR0398991
29	J Voight, Computing fundamental domains for Fuchsian groups, J. Théor. Nombres Bordeaux 21 (2009) 467 MR2541438
30	J Voight, Quaternion algebras, book project (2018)