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Embedding closed hyperbolic $3$–manifolds in small volume hyperbolic $4$–manifolds

Michelle Chu and Alan W Reid

Algebraic & Geometric Topology 21 (2021) 2627–2647
Bibliography
1 I Agol, D D Long, A W Reid, The Bianchi groups are separable on geometrically finite subgroups, Ann. of Math. 153 (2001) 599 MR1836283
2 A Basmajian, Tubular neighborhoods of totally geodesic hypersurfaces in hyperbolic manifolds, Invent. Math. 117 (1994) 207 MR1273264
3 A Borel, Harish-Chandra, Arithmetic subgroups of algebraic groups, Ann. of Math. 75 (1962) 485 MR147566
4 R Budney, B A Burton, Embeddings of 3–manifolds in S4 from the point of view of the 11–tetrahedron census, Exp. Math. (2020)
5 C Cao, G R Meyerhoff, The orientable cusped hyperbolic 3–manifolds of minimum volume, Invent. Math. 146 (2001) 451 MR1869847
6 M Chu, A W Reid, Totally geodesic hyperbolic 3-manifolds in hyperbolic link complements of tori in S4, preprint (2021) arXiv:2109.01687
7 M Culler, C M Gordon, J Luecke, P B Shalen, Dehn surgery on knots, Ann. of Math. 125 (1987) 237 MR881270
8 M Culler, W Jaco, H Rubinstein, Incompressible surfaces in once-punctured torus bundles, Proc. Lond. Math. Soc. 45 (1982) 385 MR675414
9 W Floyd, A Hatcher, Incompressible surfaces in punctured-torus bundles, Topology Appl. 13 (1982) 263 MR651509
10 D Gabai, R Meyerhoff, P Milley, Minimum volume cusped hyperbolic three-manifolds, J. Amer. Math. Soc. 22 (2009) 1157 MR2525782
11 W Hantzsche, Einlagerung von Mannigfaltigkeiten in euklidische Räume, Math. Z. 43 (1938) 38 MR1545714
12 A Hatcher, W Thurston, Incompressible surfaces in 2–bridge knot complements, Invent. Math. 79 (1985) 225 MR778125
13 D Ivanšić, Embeddability of noncompact hyperbolic manifolds as complements of codimension1 and 2 submanifolds, Topology Appl. 120 (2002) 211 MR1895493
14 D Ivanšić, Hyperbolic structure on a complement of tori in the 4–sphere, Adv. Geom. 4 (2004) 119 MR2155369
15 D Ivanšić, A topological 4–sphere that is standard, Adv. Geom. 12 (2012) 461 MR2994634
16 D Ivanšić, J G Ratcliffe, S T Tschantz, Complements of tori and Klein bottles in the 4–sphere that have hyperbolic structure, Algebr. Geom. Topol. 5 (2005) 999 MR2171801
17 R C Kirby, The topology of 4–manifolds, 1374, Springer (1989) MR1001966
18 R C Kirby editor, Problems in low-dimensional topology, from: "Geometric topology, II" (editor W H Kazez), AMS/IP Stud. Adv. Math. 2.2, Amer. Math. Soc. (1997) 35 MRMR1470751
19 A Kolpakov, A W Reid, L Slavich, Embedding arithmetic hyperbolic manifolds, Math. Res. Lett. 25 (2018) 1305 MR3882165
20 C J Leininger, Small curvature surfaces in hyperbolic 3–manifolds, J. Knot Theory Ramifications 15 (2006) 379 MR2217503
21 M T Lozano, Arcbodies, Math. Proc. Cambridge Philos. Soc. 94 (1983) 253 MR715045
22 C Maclachlan, A W Reid, The arithmetic of hyperbolic 3–manifolds, 219, Springer (2003) MR1937957
23 W Menasco, A W Reid, Totally geodesic surfaces in hyperbolic link complements, 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) 215 MR1184413
24 J J Millson, On the first Betti number of a constant negatively curved manifold, Ann. of Math. 104 (1976) 235 MR422501
25 J M Montesinos-Amilibia, On odd rank integral quadratic forms: canonical representatives of projective classes and explicit construction of integral classes with square-free determinant, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A 109 (2015) 199 MR3315712
26 U Oertel, Closed incompressible surfaces in complements of star links, Pacific J. Math. 111 (1984) 209 MR732067
27 J G Ratcliffe, S T Tschantz, Gravitational instantons of constant curvature, Classical Quantum Gravity 15 (1998) 2613 MR1649662
28 J G Ratcliffe, S T Tschantz, The volume spectrum of hyperbolic 4–manifolds, Exp. Math. 9 (2000) 101 MR1758804
29 S Riolo, L Slavich, New hyperbolic 4–manifolds of low volume, Algebr. Geom. Topol. 19 (2019) 2653 MR4023325
30 H Saratchandran, Finite volume hyperbolic complements of 2–tori and Klein bottles in closed smooth simply connected 4–manifolds, New York J. Math. 24 (2018) 443 MR3855634
31 J P Serre, A course in arithmetic, 7, Springer (1973) MR0344216
32 W P Thurston, The geometry and topology of 3–manifolds, lecture notes (1980)
33 È B Vinberg, O V Shvartsman, Discrete groups of motions of spaces of constant curvature, from: "Geometry, II : Spaces of constant curvature" (editor È B Vinberg), Encycl. Math. Sci. 29, Springer (1993) 139 MR1254933
34 Y Q Wu, Incompressibility of surfaces in surgered 3–manifolds, Topology 31 (1992) 271 MR1167169