Algebraic & Geometric Topology Volume 24, issue 5 (2024)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author index

To appear

Other MSP journals

The Burau representation and shapes of polyhedra

Ethan Dlugie

Algebraic & Geometric Topology 24 (2024) 2787–2805

DOI: 10.2140/agt.2024.24.2787

Bibliography

1	S Bigelow, The Burau representation is not faithful for n = 5, Geom. Topol. 3 (1999) 397 MR1725480
2	S J Bigelow, Braid groups are linear, J. Amer. Math. Soc. 14 (2001) 471 MR1815219
3	S Bigelow, Does the Jones polynomial detect the unknot ?, J. Knot Theory Ramifications 11 (2002) 493 MR1915491
4	J S Birman, Braids, links, and mapping class groups, 82, Princeton Univ. Press (1974) MR375281
5	W Burau, Über Zopfgruppen und gleichsinnig verdrillte Verkettungen, Abh. Math. Sem. Univ. Hamburg 11 (1935) 179 MR3069652
6	D Cooper, C D Hodgson, S P Kerckhoff, Three-dimensional orbifolds and cone-manifolds, 5, Math. Soc. Japan (2000) MR1778789
7	D Cooper, D D Long, A presentation for the image of Burau(4) ⊗ Z₂, Invent. Math. 127 (1997) 535 MR1431138
8	D Cooper, D D Long, On the Burau representation modulo a small prime, from: "The Epstein birthday schrift" (editors I Rivin, C Rourke, C Series), Geom. Topol. Monogr. 1, Geom. Topol. Publ. (1998) 127 MR1668343
9	H S M Coxeter, Factor groups of the braid group, from: "Proceedings of the fourth Canadian Mathematical Congress", Univ. Toronto Press (1959) 95 MR157845
10	P Deligne, G D Mostow, Monodromy of hypergeometric functions and nonlattice integral monodromy, Inst. Hautes Études Sci. Publ. Math. 63 (1986) 5 MR0849651
11	B Farb, D Margalit, A primer on mapping class groups, 49, Princeton Univ. Press (2012) MR2850125
12	N J Fullarton, R Shadrach, Observed periodicity related to the four-strand Burau representation, Exp. Math. 28 (2019) 57 MR3938578
13	L Funar, T Kohno, On Burau’s representations at roots of unity, Geom. Dedicata 169 (2014) 145 MR3175241
14	T Ito, A kernel of a braid group representation yields a knot with trivial knot polynomials, Math. Z. 280 (2015) 347 MR3343910
15	D Krammer, Braid groups are linear, Ann. of Math. 155 (2002) 131 MR1888796
16	D D Long, A note on the normal subgroups of mapping class groups, Math. Proc. Cambridge Philos. Soc. 99 (1986) 79 MR0809501
17	D D Long, M Paton, The Burau representation is not faithful for n ≥ 6, Topology 32 (1993) 439 MR1217079
18	C T McMullen, Braid groups and Hodge theory, Math. Ann. 355 (2013) 893 MR3020148
19	J Moody, The faithfulness question for the Burau representation, Proc. Amer. Math. Soc. 119 (1993) 671 MR1158006
20	R E Schwartz, Notes on shapes of polyhedra, preprint (2015) arXiv:1506.07252
21	C C Squier, The Burau representation is unitary, Proc. Amer. Math. Soc. 90 (1984) 199 MR0727232
22	W P Thurston, Shapes of polyhedra and triangulations of the sphere, from: "The Epstein birthday schrift" (editors I Rivin, C Rourke, C Series), Geom. Topol. Monogr. 1, Geom. Topol. Publ. (1998) 511 MR1668340
23	W A Veech, Flat surfaces, Amer. J. Math. 115 (1993) 589 MR1221838
24	T N Venkataramana, Monodromy of cyclic coverings of the projective line, Invent. Math. 197 (2014) 1 MR3219513