Three-dimensional hyperbolic manifolds with cusps of complexity 10 having maximal volume
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 2, pp. 74-87 Cet article a éte moissonné depuis la source Math-Net.Ru

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We give a complete list of three-dimensional orientable hyperbolic manifolds with cusps obtained by gluing together at most ten regular ideal hyperbolic tetrahedra. Although the list is exhaustive, the question of nonhomeomorphism remains open for some pairs of manifolds with one, two, and three cusps.
Keywords: hyperbolic manifolds with cusps, complexity of manifolds.
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A. Yu. Vesnin; V. V. Tarkaev; E. A. Fominykh. Three-dimensional hyperbolic manifolds with cusps of complexity 10 having maximal volume. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 2, pp. 74-87. http://geodesic.mathdoc.fr/item/TIMM_2014_20_2_a6/

[1] Matveev S., Algorithmic topology and classification of 3-manifolds, Algorithms and Computation in Mathematics, 9, 2nd ed., Springer, Berlin, 2007, 492 pp. | MR | Zbl

[2] Vesnin A. Yu., Matveev S. V., Fominykh E. A., “Slozhnost trekhmernykh mnogoobrazii: tochnye znacheniya i otsenki”, Sib. elektr. mat. izv., 8 (2011), 341–364 | MR

[3] Frigerio R., Martelli B., Petronio C., “Small hyperbolic 3-manifolds with geodesic boundary”, Experimental Math., 13:2 (2004), 171–184 | DOI | MR | Zbl

[4] Callahan P., Hildebrand M., Weeks J., “A census of cusped hyperbolic 3-manifolds. With microfiche supplement”, Math. Comp., 68:225 (1999), 321–332 | DOI | MR | Zbl

[5] Morwen Thistlethwaite's homepage [site]: Cusped hyperbolic manifolds with 8 tetrahedra, URL: , (data obrascheniya: 11.03.2014) http://www.math.utk.edu/~morwen/8tet/

[6] Jaco W., Rubinstein H., Tillmann S., “Minimal triangulations for an infinite family of lens spaces”, J. Topology, 2:1 (2009), 157–180 | DOI | MR | Zbl

[7] Jaco W., Rubinstein H., Tillmann S., “Coverings and minimal triangulations of 3-manifolds”, Algebr. Geom. Topol., 11:3 (2011), 1257–1265 | DOI | MR | Zbl

[8] Vesnin A. Yu., Fominykh E. A., “Tochnye znacheniya slozhnosti mnogoobrazii Paolyutsi–Tsimmermana”, Dokl. RAN, 439:6 (2011), 727–729 | MR | Zbl

[9] Vesnin A. Yu., Fominykh E. A., “O slozhnosti trekhmernykh giperbolicheskikh mnogoobrazii s geodezicheskim kraem”, Sib. mat. zhurn., 53:4 (2012), 781–793 | MR | Zbl

[10] Frigerio R., Martelli B., Petronio C., “Complexity and Heegaard genus of an infinite class of compact 3-manifolds”, Pacific J. Math., 210:2 (2003), 283–297 | DOI | MR | Zbl

[11] Anisov S., “Exact values of complexity for an infinite number of 3-manifolds”, Moscow Math. J., 5:2 (2005), 305–310 | MR | Zbl

[12] Jeff Weeks' Topology and Geometry Software [site]: SnapPea, URL: , (data obrascheniya: 11.03.2014) http://geometrygames.org/SnapPea/

[13] Hildebrand M. V., Weeks J. R., “A computer generated census of cusped hyperbolic 3-manifolds”, Computers and mathematics, Papers from the conference held at the Massachusetts Institute of Technology (Cambridge, 1989), eds. Erich Kaltofen, Stephen M. Watt, Springer-Verlag, N.Y., 1989, 53–59 | MR

[14] Burton B. A., A duplicate pair in the Snappea census, (data obrascheniya 11.03.2014), arXiv: 1311.7615

[15] Vesnin A. Yu., Tarkaev V. V., Fominykh E. A., “O slozhnosti trekhmernykh giperbolicheskikh mnogoobrazii s kaspami”, Dokl. RAN, 456:1 (2014), 11–14 | DOI

[16] Ratcliffe J., Foundations of hyperbolic manifolds, Graduate Texts in Mathematics, 149, 2nd ed., Springer, N.Y., 2006, 779 pp. | MR | Zbl

[17] Fominykh E. A., “Khirurgii Dena na uzle vosmerka: verkhnyaya otsenka slozhnosti”, Sib. mat. zhurn., 52:3 (2011), 680–689 | MR | Zbl

[18] Matveev S., Petronio C., Vesnin A., “Two-sided asymptotic bounds for the complexity of some closed hyperbolic three-manifolds”, J. Aust. Math. Soc., 86:2 (2009), 205–219 | DOI | MR | Zbl

[19] Mednykh A., Vesnin A., “Covering properties of small volume hyperbolic 3-manifolds”, J. Knot Theory Ramifications, 7:3 (1998), 381–392 | DOI | MR | Zbl

[20] Atlas of 3-Manifolds [site]: A free software 3-Manifold Recognizer, URL: , (data obrascheniya: 11.03.2014) http://matlas.math.csu.ru/

[21] Adams C., Sherman W., “Minimum ideal triangulations of hyperbolic 3-manifolds”, Discrete Comput. Geom., 6:2 (1991), 135–153 | DOI | MR | Zbl