Algebraic & Geometric Topology Volume 19, issue 5 (2019)

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New hyperbolic $4$–manifolds of low volume

Stefano Riolo and Leone Slavich

Algebraic & Geometric Topology 19 (2019) 2653–2676

DOI: 10.2140/agt.2019.19.2653

Bibliography

1	C C Adams, The noncompact hyperbolic 3–manifold of minimal volume, Proc. Amer. Math. Soc. 100 (1987) 601 MR894423
2	M Conder, C Maclachlan, Compact hyperbolic 4–manifolds of small volume, Proc. Amer. Math. Soc. 133 (2005) 2469 MR2138890
3	H S M Coxeter, Regular polytopes, Macmillan (1963) MR0151873
4	D Gabai, R Meyerhoff, P Milley, Minimum volume cusped hyperbolic three-manifolds, J. Amer. Math. Soc. 22 (2009) 1157 MR2525782
5	M Gromov, I Piatetski-Shapiro, Nonarithmetic groups in Lobachevsky spaces, Inst. Hautes Études Sci. Publ. Math. 66 (1988) 93 MR932135
6	R Guglielmetti, M Jacquemet, R Kellerhals, On commensurable hyperbolic Coxeter groups, Geom. Dedicata 183 (2016) 143 MR3523123
7	S P Kerckhoff, P A Storm, From the hyperbolic 24–cell to the cuboctahedron, Geom. Topol. 14 (2010) 1383 MR2653730
8	A Kolpakov, On the optimality of the ideal right-angled 24–cell, Algebr. Geom. Topol. 12 (2012) 1941 MR2994826
9	A Kolpakov, L Slavich, Symmetries of hyperbolic 4–manifolds, Int. Math. Res. Not. 2016 (2016) 2677 MR3519127
10	C Long, Small volume closed hyperbolic 4–manifolds, Bull. Lond. Math. Soc. 40 (2008) 913 MR2439657
11	C Maclachlan, Commensurability classes of discrete arithmetic hyperbolic groups, Groups Geom. Dyn. 5 (2011) 767 MR2836459
12	G A Margulis, Discrete subgroups of semisimple Lie groups, 17, Springer (1991) MR1090825
13	B. Martelli, An introduction to geometric topology, book project (2016)
14	B Martelli, Hyperbolic four-manifolds, from: "Handbook of group actions, III" (editors L Ji, A Papadopoulos, S T Yau), Adv. Lect. Math. 40, International (2018) 37 MR3888615
15	B Martelli, S Riolo, Hyperbolic Dehn filling in dimension four, Geom. Topol. 22 (2018) 1647 MR3780443
16	S V Matveev, A T Fomenko, Isoenergetic surfaces of Hamiltonian systems, the enumeration of three-dimensional manifolds in order of growth of their complexity, and the calculation of the volumes of closed hyperbolic manifolds, Uspekhi Mat. Nauk 43 (1988) 5 MR937017
17	J G Ratcliffe, Foundations of hyperbolic manifolds, 149, Springer (1994) MR1299730
18	J G Ratcliffe, S T Tschantz, The volume spectrum of hyperbolic 4–manifolds, Experiment. Math. 9 (2000) 101 MR1758804
19	L Slavich, The complement of the figure-eight knot geometrically bounds, Proc. Amer. Math. Soc. 145 (2017) 1275 MR3589325
20	W P Thurston, The geometry and topology of three-manifolds, lecture notes (1979)
21	P V Tumarkin, Hyperbolic Coxeter n–polytopes with n + 2 facets, Mat. Zametki 75 (2004) 909 MR2086616
22	È B Vinberg, Hyperbolic reflection groups, Uspekhi Mat. Nauk 40 (1985) 29, 255 MR783604
23	H C Wang, Topics on totally discontinuous groups, from: "Symmetric spaces" (editors W M Boothby, G L Weiss), Pure and Appl. Math. 8, Dekker (1972) 459 MR0414787
24	J. Weeks, Hyperbolic structures on 3–manifolds, PhD thesis, Princeton University (1985)