Geometry & Topology Volume 19, issue 5 (2015)

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

$1$–efficient triangulations and the index of a cusped hyperbolic $3$–manifold

Stavros Garoufalidis, Craig D Hodgson, J Hyam Rubinstein and Henry Segerman

Geometry & Topology 19 (2015) 2619–2689

DOI: 10.2140/gt.2015.19.2619

Bibliography

1	H Akiyoshi, Finiteness of polyhedral decompositions of cusped hyperbolic manifolds obtained by the Epstein–Penner’s method, Proc. Amer. Math. Soc. 129 (2001) 2431 MR1823928
2	J E Andersen, R Kashaev, A TQFT from Quantum Teichmüller theory, Comm. Math. Phys. 330 (2014) 887 MR3227503
3	S Baseilhac, R Benedetti, Classical and quantum dilogarithmic invariants of flat PSL(2, ℂ)–bundles over 3–manifolds, Geom. Topol. 9 (2005) 493 MR2140989
4	S Baseilhac, R Benedetti, Quantum hyperbolic geometry, Algebr. Geom. Topol. 7 (2007) 845 MR2336244
5	C Beem, T Dimofte, S Pasquetti, Holomorphic blocks in three dimensions, J. High Energy Phys. 2014 (2014) MR3303415
6	R Benedetti, C Petronio, Branched standard spines of 3–manifolds, 1653, Springer (1997) MR1470454
7	D Cooper, M Culler, H Gillet, D D Long, P B Shalen, Plane curves associated to character varieties of 3–manifolds, Invent. Math. 118 (1994) 47 MR1288467
8	M Culler, N M Dunfield, J R Weeks, SnapPy, a computer program for studying the topology of 3–manifolds
9	J A De Loera, J Rambau, F Santos, Triangulations: Structures for algorithms and applications, 25, Springer (2010) MR2743368
10	T Dimofte, D Gaiotto, S Gukov, 3–manifolds and 3d indices, Adv. Theor. Math. Phys. 17 (2013) 975 MR3262519
11	T Dimofte, D Gaiotto, S Gukov, Gauge theories labelled by three-manifolds, Comm. Math. Phys. 325 (2014) 367 MR3148093
12	T Dimofte, S Garoufalidis, The quantum content of the gluing equations, Geom. Topol. 17 (2013) 1253 MR3073925
13	D B A Epstein, R C Penner, Euclidean decompositions of noncompact hyperbolic manifolds, J. Differential Geom. 27 (1988) 67 MR918457
14	C Frohman, J Kania-Bartoszynska, The quantum content of the normal surfaces in a three-manifold, J. Knot Theory Ramifications 17 (2008) 1005 MR2439773
15	S Garoufalidis, 3D index data
16	S Garoufalidis, The 3D index of an ideal triangulation and angle structures, arXiv:1208.1663
17	S Garoufalidis, R Kashaev, From state-integrals to q–series, arXiv:1304.2705
18	S Garoufalidis, T T Lê, Nahm sums, stability and the colored Jones polynomial, Res. Math. Sci. 2 (2015) MR3375651
19	S Garoufalidis, T Vuong, Alternating knots, planar graphs, and q–series, Ramanujan J. 36 (2015) 501 MR3317869
20	S Garoufalidis, D Zagier, Empirical relations between q–series and Kashaev’s invariant of knots (2013)
21	I M Gel′fand, M M Kapranov, A V Zelevinsky, Discriminants, resultants, and multidimensional determinants, Birkhäuser (1994) MR1264417
22	F Guéritaud, S Schleimer, Canonical triangulations of Dehn fillings, Geom. Topol. 14 (2010) 193 MR2578304
23	A Hatcher, Notes on basic 3–manifold topology (2007)
24	C D Hodgson, J H Rubinstein, H Segerman, Triangulations of hyperbolic 3–manifolds admitting strict angle structures, J. Topol. 5 (2012) 887 MR3001314
25	W Jaco, J H Rubinstein, 0–efficient triangulations of 3–manifolds, J. Differential Geom. 65 (2003) 61 MR2057531
26	V F R Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. 126 (1987) 335 MR908150
27	E Kang, J H Rubinstein, Ideal triangulations of 3–manifolds, I : Spun normal surface theory, from: "Proceedings of the Casson Fest" (editors C Gordon, Y Rieck), Geom. Topol. Monogr. 7 (2004) 235 MR2172486
28	E Kang, J H Rubinstein, Ideal triangulations of 3–manifolds, II : Taut and angle structures, Algebr. Geom. Topol. 5 (2005) 1505 MR2186107
29	R M Kashaev, The hyperbolic volume of knots from the quantum dilogarithm, Lett. Math. Phys. 39 (1997) 269 MR1434238
30	R Kashaev, F Luo, G Vartanov, A TQFT of Turaev–Viro type on shaped triangulations, arXiv:1210.8393
31	M Lackenby, Taut ideal triangulations of 3–manifolds, Geom. Topol. 4 (2000) 369 MR1790190
32	M Lackenby, Word hyperbolic Dehn surgery, Invent. Math. 140 (2000) 243 MR1756996
33	M Lackenby, An algorithm to determine the Heegaard genus of simple 3–manifolds with nonempty boundary, Alg. Geom. Topol. 8 (2008) 911
34	J L Loday, Realization of the Stasheff polytope, Arch. Math. (Basel) 83 (2004) 267 MR2108555
35	F Luo, S Tillmann, Angle structures and normal surfaces, Trans. Amer. Math. Soc. 360 (2008) 2849 MR2379778
36	S MacLane, Categories for the working mathematician, 5, Springer (1971) MR0354798
37	S V Matveev, Transformations of special spines, and the Zeeman conjecture, Izv. Akad. Nauk SSSR Ser. Mat. 51 (1987) 1104, 1119 MR925096
38	S Matveev, Algorithmic topology and classification of 3–manifolds, 9, Springer (2007) MR2341532
39	W D Neumann, Combinatorics of triangulations and the Chern–Simons invariant for hyperbolic 3–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) 243 MR1184397
40	W D Neumann, D Zagier, Volumes of hyperbolic three-manifolds, Topology 24 (1985) 307 MR815482
41	C Petronio, Standard spines and 3–manifolds, PhD thesis, Scuola Normale Superiore, Pisa (1995)
42	R Piergallini, Standard moves for standard polyhedra and spines, Rend. Circ. Mat. Palermo Suppl. (1988) 391 MR958750
43	J H Rubinstein, Polyhedral minimal surfaces, Heegaard splittings and decision problems for 3–dimensional manifolds, from: "Geometric topology" (editor W H Kazez), AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 1 MR1470718
44	F Santos, Geometric bistellar flips: The setting, the context and a construction, from: "International Congress of Mathematicians, Vol. III" (editors M Sanz-Solé, J Soria, J L Varona, J Verdera), Eur. Math. Soc. (2006) 931 MR2275713
45	J D Stasheff, Homotopy associativity of H–spaces, I, II, Trans. Amer. Math. Soc. 108, 275-292; ibid. 108 (1963) 293 MR0158400
46	J Stasheff, From operads to “physically” inspired theories, from: "Operads : Proceedings of Renaissance Conferences" (editors J L Loday, J D Stasheff, A A Voronov), Contemp. Math. 202, Amer. Math. Soc. (1997) 53 MR1436917
47	M Stocking, Almost normal surfaces in 3–manifolds, Trans. Amer. Math. Soc. 352 (2000) 171 MR1491877
48	W P Thurston, The geometry and topology of three-manifolds, lecture notes (1979)
49	J Weeks, Hyperbolic structures on three-manifolds, PhD thesis, Princeton Univ. (1985)