Algebraic & Geometric Topology Volume 25, issue 8 (2025)

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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Crushing surfaces of positive genus

Benjamin A Burton, Thiago de Paiva, Alexander He and Connie On Yu Hui

Algebraic & Geometric Topology 25 (2025) 4949–5012

DOI: 10.2140/agt.2025.25.4949

Bibliography

1	M Bucher, R Frigerio, C Pagliantini, The simplicial volume of 3-manifolds with boundary, J. Topol. 8 (2015) 457 MR3356768
2	B A Burton, Computational topology with Regina : algorithms, heuristics and implementations, from: "Geometry and topology down under" (editors C D Hodgson, W H Jaco, M G Scharlemann, S Tillmann), Contemp. Math. 597, Amer. Math. Soc. (2013) 195 MR3186674
3	B A Burton, A new approach to crushing 3-manifold triangulations, Discrete Comput. Geom. 52 (2014) 116 MR3231034
4	B A Burton, R Budney, W Pettersson, others, Regina : Software for low-dimensional topology
5	B A Burton, A Coward, S Tillmann, Computing closed essential surfaces in knot complements, from: "Computational geometry" (editors G D d Fonseca, T Lewiner, L Peñaranda), ACM (2013) 405 MR3208239
6	B A Burton, A He, Finding large counterexamples by selectively exploring the Pachner graph, from: "39th International Symposium on Computational Geometry" (editors E W Chambers, J Gudmundsson), LIPIcs. Leibniz Int. Proc. Inform. 258, Schloss Dagstuhl. Leibniz-Zent. Inform. (2023) 21 MR4604006
7	B A Burton, M Ozlen, A fast branching algorithm for unknot recognition with experimental polynomial-time behaviour, preprint (2014) arXiv:1211.1079v3
8	B A Burton, S Tillmann, Computing closed essential surfaces in 3-manifolds, J. Appl. Comput. Topol. 9 (2025) 18 MR4925295
9	J Fowler, Finding 0-efficient triangulations of 3-manifolds, senior honors thesis, Harvard University (2003)
10	A Hatcher, Notes on basic 3-manifold topology,
11	C O Y Hui, A geometric classification of rod complements in the 3-torus, Proc. Amer. Math. Soc. 153 (2025) 381 MR4840285
12	C O Y Hui, J S Purcell, On the geometry of rod packings in the 3-torus, Bull. Lond. Math. Soc. 56 (2024) 1291 MR4735618
13	K Ichihara, Y Nishimura, S Tani, The computational complexity of classical knot recognition, J. Knot Theory Ramifications 32 (2023) 2350069 MR4683261
14	A Jackson, Minimal triangulation size of Seifert fibered spaces with boundary, preprint (2023) arXiv:2301.02085
15	W Jaco, J Johnson, J Spreer, S Tillmann, Bounds for the genus of a normal surface, Geom. Topol. 20 (2016) 1625 MR3523065
16	W Jaco, H Rubinstein, J Spreer, S Tillmann, On minimal ideal triangulations of cusped hyperbolic 3-manifolds, J. Topol. 13 (2020) 308 MR4138740
17	W Jaco, H Rubinstein, S Tillmann, Minimal triangulations for an infinite family of lens spaces, J. Topol. 2 (2009) 157 MR2499441
18	W Jaco, J H Rubinstein, 0-efficient triangulations of 3-manifolds, J. Differential Geom. 65 (2003) 61 MR2057531
19	W Jaco, J H Rubinstein, J Spreer, S Tillmann, ℤ₂-Thurston norm and complexity of 3-manifolds, II, Algebr. Geom. Topol. 20 (2020) 503 MR4071382
20	W Jaco, J H Rubinstein, J Spreer, S Tillmann, Complexity of 3-manifolds obtained by Dehn filling, Algebr. Geom. Topol. 25 (2025) 301 MR4877259
21	W Jaco, J H Rubinstein, S Tillmann, Coverings and minimal triangulations of 3-manifolds, Algebr. Geom. Topol. 11 (2011) 1257 MR2801418
22	W Jaco, J H Rubinstein, S Tillmann, ℤ₂-Thurston norm and complexity of 3-manifolds, Math. Ann. 356 (2013) 1 MR3038119
23	W Jaco, P B Shalen, A new decomposition theorem for irreducible sufficiently-large 3-manifolds, from: "Algebraic and geometric topology, part 2" (editor R J Milgram), Proc. Sympos. Pure Math. 32, Amer. Math. Soc. (1978) 71 MR520524
24	W H Jaco, P B Shalen, Seifert fibered spaces in 3-manifolds, 220 (1979) MR539411
25	K Johannson, Homotopy equivalences of 3-manifolds with boundaries, 761, Springer (1979) MR551744
26	M Lackenby, J S Purcell, The triangulation complexity of elliptic and sol 3-manifolds, Math. Ann. 390 (2024) 1623 MR4801816
27	M Lackenby, J S Purcell, The triangulation complexity of fibred 3-manifolds, Geom. Topol. 28 (2024) 1727 MR4777702
28	S Matveev, Algorithmic topology and classification of 3-manifolds, 9, Springer (2007) MR2341532
29	M O’Keeffe, J Plévert, T Ogawa, Homogeneous cubic cylinder packings revisited, Acta Crystallogr. Sect. A 58 (2002) 125 MR1897189
30	M O’Keeffe, J Plévert, Y Teshima, Y Watanabe, T Ogama, The invariant cubic rod (cylinder) packings : symmetries and coordinates, Acta Cryst. Sect. A 57 (2001) 110 MR1805573
31	J S Purcell, Hyperbolic knot theory, 209, Amer. Math. Soc. (2020) MR4249621
32	J H Rubinstein, J Spreer, S Tillmann, A new family of minimal ideal triangulations of cusped hyperbolic 3-manifolds, from: "2021–2022 MATRIX annals" (editors D R Wood, J d Gier, C E Praeger), MATRIX Book Ser. 5, Springer (2024) 5 MR4807266
33	A Y Vesnin, E A Fominykh, Exact values of complexity for Paoluzzi–Zimmermann manifolds, Dokl. Math. (2011) 542 MR2883799