Geometry & Topology Volume 22, issue 6 (2018)

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

Generators for a complex hyperbolic braid group

Daniel Allcock and Tathagata Basak

Geometry & Topology 22 (2018) 3435–3500

DOI: 10.2140/gt.2018.22.3435

Bibliography

1	D Allcock, The Leech lattice and complex hyperbolic reflections, Invent. Math. 140 (2000) 283 MR1756997
2	D Allcock, A monstrous proposal, from: "Groups and symmetries: from neolithic Scots to John McKay" (editors J Harnad, P Winternitz), CRM Proc. Lecture Notes 47, Amer. Math. Soc. (2009) 17 MR2500552
3	D Allcock, On the Y ₅₅₅ complex reflection group, J. Algebra 322 (2009) 1454 MR2543618
4	D Allcock, Completions, branched covers, Artin groups, and singularity theory, Duke Math. J. 162 (2013) 2645 MR3127810
5	D Allcock, T Basak, Geometric generators for braid-like groups, Geom. Topol. 20 (2016) 747 MR3493096
6	D Allcock, J A Carlson, D Toledo, The complex hyperbolic geometry of the moduli space of cubic surfaces, J. Algebraic Geom. 11 (2002) 659 MR1910264
7	D Allcock, J A Carlson, D Toledo, The moduli space of cubic threefolds as a ball quotient, 985, Amer. Math. Soc. (2011) MR2789835
8	E Bannai, Fundamental groups of the spaces of regular orbits of the finite unitary reflection groups of dimension 2, J. Math. Soc. Japan 28 (1976) 447 MR0407199
9	T Basak, The complex Lorentzian Leech lattice and the bimonster, J. Algebra 309 (2007) 32 MR2301231
10	T Basak, On Coxeter diagrams of complex reflection groups, Trans. Amer. Math. Soc. 364 (2012) 4909 MR2922614
11	T Basak, The complex Lorentzian Leech lattice and the bimonster, II, Trans. Amer. Math. Soc. 368 (2016) 4171 MR3453368
12	C Batut, K Belabas, D Benardi, H Cohen, M Olivier, User’s guide to PARI/GP, (2016)
13	D Bessis, Finite complex reflection arrangements are K(π,1), Ann. of Math. 181 (2015) 809 MR3296817
14	M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
15	E Brieskorn, Die Fundamentalgruppe des Raumes der regulären Orbits einer endlichen komplexen Spiegelungsgruppe, Invent. Math. 12 (1971) 57 MR0293615
16	E Brieskorn, Vue d’ensemble sur les problèmes de monodromie, from: "Singularités à Cargèse (rencontre sur les singularités en géométrie analytique)", Astérisque 7 et 8, Soc. Math. France (1973) 393 MR0417168
17	M Broué, Introduction to complex reflection groups and their braid groups, 1988, Springer (2010) MR2590895
18	J H Conway, R T Curtis, S P Norton, R A Parker, R A Wilson, Atlas of finite groups: maximal subgroups and ordinary characters for simple groups, Oxford Univ. Press (1985) MR827219
19	J H Conway, C S Simons, 26 implies the Bimonster, J. Algebra 235 (2001) 805 MR1805481
20	J H Conway, N J A Sloane, Sphere packings, lattices and groups, 290, Springer (1999) MR1662447
21	R Fox, L Neuwirth, The braid groups, Math. Scand. 10 (1962) 119 MR0150755
22	W M Goldman, Complex hyperbolic geometry, Oxford Univ. Press (1999) MR1695450
23	R Laza, Deformations of singularities and variation of GIT quotients, Trans. Amer. Math. Soc. 361 (2009) 2109 MR2465831
24	H van der Lek, The homotopy type of complex hyperplane complements, PhD thesis, Katholieke Universiteit Nijmegen (1983)
25	A Libgober, On the fundamental group of the space of cubic surfaces, Math. Z. 162 (1978) 63 MR505917
26	M Lönne, Fundamental group of discriminant complements of Brieskorn–Pham polynomials, C. R. Math. Acad. Sci. Paris 345 (2007) 93 MR2343559
27	E Looijenga, The smoothing components of a triangle singularity, II, Math. Ann. 269 (1984) 357 MR761312
28	E Looijenga, Compactifications defined by arrangements, II : Locally symmetric varieties of type IV, Duke Math. J. 119 (2003) 527 MR2003125
29	E Looijenga, Artin groups and the fundamental groups of some moduli spaces, J. Topol. 1 (2008) 187 MR2365657
30	P Orlik, L Solomon, Discriminants in the invariant theory of reflection groups, Nagoya Math. J. 109 (1988) 23 MR931949
31	R A Wilson, The complex Leech lattice and maximal subgroups of the Suzuki group, J. Algebra 84 (1983) 151 MR716777