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Bounds on Pachner moves and systoles of cusped $3$–manifolds

Tejas Kalelkar and Sriram Raghunath

Algebraic & Geometric Topology 22 (2022) 2951–2996
DOI: 10.2140/agt.2022.22.2951
Bibliography
1 C C Adams, Waist size for cusps in hyperbolic 3–manifolds, Topology 41 (2002) 257 MR1876890
2 C Adams, J Hass, P Scott, Simple closed geodesics in hyperbolic 3–manifolds, Bull. London Math. Soc. 31 (1999) 81 MR1650997
3 C C Adams, A W Reid, Systoles of hyperbolic 3–manifolds, Math. Proc. Cambridge Philos. Soc. 128 (2000) 103 MR1724432
4 K A Adiprasito, B Benedetti, Subdivisions, shellability, and collapsibility of products, Combinatorica 37 (2017) 1 MR3638330
5 G Amendola, A calculus for ideal triangulations of three-manifolds with embedded arcs, Math. Nachr. 278 (2005) 975 MR2150371
6 R Benedetti, C Petronio, Lectures on hyperbolic geometry, Springer (1992) MR1219310
7 W Breslin, Thick triangulations of hyperbolic n–manifolds, Pacific J. Math. 241 (2009) 215 MR2507575
8 B A Burton, A duplicate pair in the SnapPea census, Exp. Math. 23 (2014) 170 MR3223771
9 C Cao, G R Meyerhoff, The orientable cusped hyperbolic 3–manifolds of minimum volume, Invent. Math. 146 (2001) 451 MR1869847
10 A Coward, M Lackenby, An upper bound on Reidemeister moves, Amer. J. Math. 136 (2014) 1023 MR3245186
11 B Dadd, A Duan, Constructing infinitely many geometric triangulations of the figure eight knot complement, Proc. Amer. Math. Soc. 144 (2016) 4545 MR3531201
12 D B A Epstein, R C Penner, Euclidean decompositions of noncompact hyperbolic manifolds, J. Differential Geom. 27 (1988) 67 MR918457
13 D Futer, J S Purcell, Links with no exceptional surgeries, Comment. Math. Helv. 82 (2007) 629 MR2314056
14 C M Gordon, J Luecke, Knots are determined by their complements, J. Amer. Math. Soc. 2 (1989) 371 MR965210
15 W Haken, Some results on surfaces in 3–manifolds, from: "Studies in modern topology" (editor P J Hilton), Math. Assoc. Amer. (1968) 39 MR0224071
16 S L Ham, J S Purcell, Geometric triangulations and highly twisted links, preprint (2020) arXiv:2005.11899
17 G Hemion, On the classification of homeomorphisms of 2–manifolds and the classification of 3–manifolds, Acta Math. 142 (1979) 123 MR512214
18 J Hoste, M Thistlethwaite, J Weeks, The first 1,701,936 knots, Math. Intelligencer 20 (1998) 33 MR1646740
19 I Izmestiev, J M Schlenker, Infinitesimal rigidity of polyhedra with vertices in convex position, Pacific J. Math. 248 (2010) 171 MR2734170
20 T Kalelkar, A Phanse, Geometric bistellar moves relate geometric triangulations, Topology Appl. 285 (2020) 1 MR4152822
21 T Kalelkar, A Phanse, An upper bound on Pachner moves relating geometric triangulations, Discrete Comput. Geom. 66 (2021) 809 MR4310596
22 G Kuperberg, Algorithmic homeomorphism of 3–manifolds as a corollary of geometrization, Pacific J. Math. 301 (2019) 189 MR4007377
23 M Lackenby, The volume of hyperbolic alternating link complements, Proc. London Math. Soc. 88 (2004) 204 MR2018964
24 W B R Lickorish, Unshellable triangulations of spheres, European J. Combin. 12 (1991) 527 MR1136394
25 W B R Lickorish, Simplicial moves on complexes and manifolds, from: "Proceedings of the Kirbyfest" (editors J Hass, M Scharlemann), Geom. Topol. Monogr. 2, Geom. Topol. Publ. (1999) 299 MR1734414
26 F Luo, S Schleimer, S Tillmann, Geodesic ideal triangulations exist virtually, Proc. Amer. Math. Soc. 136 (2008) 2625 MR2390535
27 J Manning, Algorithmic detection and description of hyperbolic structures on closed 3–manifolds with solvable word problem, Geom. Topol. 6 (2002) 1 MR1885587
28 S Matveev, Algorithmic topology and classification of 3–manifolds, 9, Springer (2007) MR2341532
29 W Menasco, Closed incompressible surfaces in alternating knot and link complements, Topology 23 (1984) 37 MR721450
30 A Mijatović, Simplical structures of knot complements, Math. Res. Lett. 12 (2005) 843 MR2189244
31 G D Mostow, Strong rigidity of locally symmetric spaces, 78, Princeton Univ. Press (1973) MR0385004
32 G Prasad, Strong rigidity of Q–rank 1 lattices, Invent. Math. 21 (1973) 255 MR385005
33 M E Rudin, An unshellable triangulation of a tetrahedron, Bull. Amer. Math. Soc. 64 (1958) 90 MR97055
34 Z Sela, The isomorphism problem for hyperbolic groups, I, Ann. of Math. 141 (1995) 217 MR1324134
35 P B Shalen, A generic Margulis number for hyperbolic 3–manifolds, 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) 103 MR2866926
36 J R Weeks, Convex hulls and isometries of cusped hyperbolic 3–manifolds, Topology Appl. 52 (1993) 127 MR1241189