Download this article
 Download this article For screen
For printing
Recent Issues

Volume 25
Issue 6, 3145–3787
Issue 5, 2527–3144
Issue 4, 1917–2526
Issue 3, 1265–1915
Issue 2, 645–1264
Issue 1, 1–644

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 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
Complexity of $3$-manifolds obtained by Dehn filling

William Jaco, Joachim Hyam Rubinstein, Jonathan Spreer and Stephan Tillmann

Algebraic & Geometric Topology 25 (2025) 301–327
Bibliography
1 B A Burton, R Budney, W Pettersson, others, Regina: software for low-dimensional topology (1999–2021)
2 B A Burton, J H Rubinstein, S Tillmann, The Weber–Seifert dodecahedral space is non-Haken, Trans. Amer. Math. Soc. 364 (2012) 911 MR2846358
3 J C Cha, Complexity of surgery manifolds and Cheeger–Gromov invariants, Int. Math. Res. Not. 2016 (2016) 5603 MR3567253
4 J C Cha, A topological approach to Cheeger–Gromov universal bounds for von Neumann ρ-invariants, Comm. Pure Appl. Math. 69 (2016) 1154 MR3493628
5 J C Cha, Complexities of 3-manifolds from triangulations, Heegaard splittings and surgery presentations, Q. J. Math. 69 (2018) 425 MR3811586
6 M Culler, N M Dunfield, M Goerner, J R Weeks, SnapPy, a computer program for studying the geometry and topology of 3-manifolds
7 N M Dunfield, A census of exceptional Dehn fillings, from: "Characters in low-dimensional topology", Contemp. Math. 760, Amer. Math. Soc. (2020) 143 MR4193924
8 E Fominykh, S Garoufalidis, M Goerner, V Tarkaev, A Vesnin, A census of tetrahedral hyperbolic manifolds, Exp. Math. 25 (2016) 466 MR3499710
9 R Frigerio, B Martelli, C Petronio, Dehn filling of cusped hyperbolic 3-manifolds with geodesic boundary, J. Differential Geom. 64 (2003) 425 MR2032111
10 J Hass, J C Lagarias, N Pippenger, The computational complexity of knot and link problems, J. ACM 46 (1999) 185 MR1693203
11 A E Hatcher, On the boundary curves of incompressible surfaces, Pacific J. Math. 99 (1982) 373 MR658066
12 M Ishikawa, K Nemoto, Construction of spines of two-bridge link complements and upper bounds of their Matveev complexities, Hiroshima Math. J. 46 (2016) 149 MR3536993
13 W Jaco, J Johnson, J Spreer, S Tillmann, Bounds for the genus of a normal surface, Geom. Topol. 20 (2016) 1625 MR3523065
14 W Jaco, J H Rubinstein, Inflations of ideal triangulations, Adv. Math. 267 (2014) 176 MR3269178
15 W Jaco, J H Rubinstein, J Spreer, S Tillmann, 2-Thurston norm and complexity of 3-manifolds, II, Algebr. Geom. Topol. 20 (2020) 503 MR4071382
16 W Jaco, J H Rubinstein, J Spreer, S Tillmann, On minimal ideal triangulations of cusped hyperbolic 3-manifolds, J. Topol. 13 (2020) 308 MR4138740
17 W Jaco, J H Rubinstein, J Spreer, S Tillmann, Slope norm and an algorithm to compute the crosscap number, Algebr. Geom. Topol. 24 (2024) 4307 MR4843732
18 W Jaco, J H Rubinstein, S Tillmann, Minimal triangulations for an infinite family of lens spaces, J. Topol. 2 (2009) 157 MR2499441
19 W Jaco, J H Rubinstein, S Tillmann, 2-Thurston norm and complexity of 3-manifolds, Math. Ann. 356 (2013) 1 MR3038119
20 W Jaco, E Sedgwick, Decision problems in the space of Dehn fillings, Topology 42 (2003) 845 MR1958532
21 M Lackenby, J S Purcell, The triangulation complexity of fibred 3-manifolds, Geom. Topol. 28 (2024) 1727 MR4777702
22 W B R Lickorish, A representation of orientable combinatorial 3-manifolds, Ann. of Math. 76 (1962) 531 MR151948
23 S V Matveev, Complexity theory of three-dimensional manifolds, Acta Appl. Math. 19 (1990) 101 MR1074221
24 S V Matveev, E L Pervova, Lower bounds for the complexity of three-dimensional manifolds, Dokl. Akad. Nauk 378 (2001) 151 MR1863880
25 S Matveev, C Petronio, A Vesnin, Two-sided asymptotic bounds for the complexity of some closed hyperbolic three-manifolds, J. Aust. Math. Soc. 86 (2009) 205 MR2507595
26 S V Matveev, V V Tarkaev, Recognition and tabulation of 3-manifolds up to complexity 13, Chebyshevskiĭ Sb. 21 (2020) 290 MR4188509
27 E Pervova, C Petronio, Complexity and T-invariant of abelian and Milnor groups, and complexity of 3-manifolds, Math. Nachr. 281 (2008) 1182 MR2427169
28 C Petronio, A Vesnin, Two-sided bounds for the complexity of cyclic branched coverings of two-bridge links, Osaka J. Math. 46 (2009) 1077 MR2604922
29 J H Rubinstein, J Spreer, S Tillmann, A new family of minimal ideal triangulations of cusped hyperbolic 3-manifolds, from: "20212022 MATRIX annals", MATRIX Book Ser. 5, Springer (2024) 5
30 W P Thurston, The geometry and topology of three-manifolds, lecture notes (1979)
31 A Y Vesnin, V V Tarkaev, E A Fominykh, Three-dimensional hyperbolic manifolds with cusps of complexity 10 that have maximal volume, Tr. Inst. Mat. Mekh. 20 (2014) 74 MR3364141
32 A H Wallace, Modifications and cobounding manifolds, IV, J. Math. Mech. 12 (1963) 445 MR154297
33 J Weeks, Computation of hyperbolic structures in knot theory, from: "Handbook of knot theory", Elsevier (2005) 461 MR2179268