Algebraic & Geometric Topology Volume 23, issue 3 (2023)

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

Geometric triangulations and highly twisted links

Sophie L Ham and Jessica S Purcell

Algebraic & Geometric Topology 23 (2023) 1399–1462

DOI: 10.2140/agt.2023.23.1399

Bibliography

1	I Agol, Ideal triangulations of pseudo-Anosov mapping tori, from: "Topology and geometry in dimension three" (editors W Li, L Bartolini, J Johnson, F Luo, R Myers, J H Rubinstein), Contemp. Math. 560, Amer. Math. Soc. (2011) 1 MR2866919
2	I Agol, D Thurston, (2004) MR2018964
3	R Benedetti, C Petronio, Lectures on hyperbolic geometry, Springer (1992) MR1219310
4	R H Bing, An alternative proof that 3–manifolds can be triangulated, Ann. of Math. 69 (1959) 37 MR100841
5	Y E Choi, Positively oriented ideal triangulations on hyperbolic three-manifolds, Topology 43 (2004) 1345 MR2081429
6	M Culler, N M Dunfield, J R Weeks, SnapPy, a computer program for studying the topology of 3–manifolds
7	D B A Epstein, R C Penner, Euclidean decompositions of noncompact hyperbolic manifolds, J. Differential Geom. 27 (1988) 67 MR918457
8	D Futer, F Guéritaud, From angled triangulations to hyperbolic structures, 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) 159 MR2796632
9	D Futer, F Guéritaud, Explicit angle structures for veering triangulations, Algebr. Geom. Topol. 13 (2013) 205 MR3031641
10	D Futer, E Kalfagianni, J S Purcell, Dehn filling, volume, and the Jones polynomial, J. Differential Geom. 78 (2008) 429 MR2396249
11	D Futer, J S Purcell, Links with no exceptional surgeries, Comment. Math. Helv. 82 (2007) 629 MR2314056
12	D Futer, S J Taylor, W Worden, Random veering triangulations are not geometric, Groups Geom. Dyn. 14 (2020) 1077 MR4167033
13	M Goerner, A census of hyperbolic platonic manifolds and augmented knotted trivalent graphs, New York J. Math. 23 (2017) 527 MR3665576
14	M Goerner, Geodesic triangulations exist for cusped Platonic manifolds, New York J. Math. 23 (2017) 1363 MR3723513
15	F Guéritaud, On canonical triangulations of once-punctured torus bundles and two-bridge link complements, Geom. Topol. 10 (2006) 1239 MR2255497
16	F Guéritaud, S Schleimer, Canonical triangulations of Dehn fillings, Geom. Topol. 14 (2010) 193 MR2578304
17	C D Hodgson, A Issa, H Segerman, Non-geometric veering triangulations, Exp. Math. 25 (2016) 17 MR3424830
18	C D Hodgson, J H Rubinstein, H Segerman, Triangulations of hyperbolic 3–manifolds admitting strict angle structures, J. Topol. 5 (2012) 887 MR3001314
19	C D Hodgson, J H Rubinstein, H Segerman, S Tillmann, Veering triangulations admit strict angle structures, Geom. Topol. 15 (2011) 2073 MR2860987
20	W Jaco, J H Rubinstein, Layered-triangulations of 3–manifolds, preprint (2006) arXiv:math/0603601
21	F Luo, S Schleimer, S Tillmann, Geodesic ideal triangulations exist virtually, Proc. Amer. Math. Soc. 136 (2008) 2625 MR2390535
22	E E Moise, Affine structures in 3–manifolds, V : The triangulation theorem and Hauptvermutung, Ann. of Math. 56 (1952) 96 MR48805
23	W D Neumann, D Zagier, Volumes of hyperbolic three-manifolds, Topology 24 (1985) 307 MR815482
24	C Petronio, J Porti, Negatively oriented ideal triangulations and a proof of Thurston’s hyperbolic Dehn filling theorem, Expo. Math. 18 (2000) 1 MR1751141
25	J S Purcell, Cusp shapes under cone deformation, J. Differential Geom. 80 (2008) 453 MR2472480
26	J S Purcell, Slope lengths and generalized augmented links, Comm. Anal. Geom. 16 (2008) 883 MR2471374
27	J S Purcell, An introduction to fully augmented links, 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) 205 MR2796634
28	I Rivin, Euclidean structures on simplicial surfaces and hyperbolic volume, Ann. of Math. 139 (1994) 553 MR1283870
29	W P Thurston, The geometry and topology of three-manifolds, lecture notes (1979)