The Volume Spectrum of Hyperbolic 4-Manifolds

REFERENCES

• Bianchi , L. 1892 . “Sui gruppi di sostituzioni lineari con coefficient! appartenenti a corpi quadratici immaginari” . Math. Ann. , 40 : 332 – 412 . [Bianchi 1892]
   Google Scholar
• Brunner , A. M. , Frame , M. L. , Lee , Y. W. and Wielenberg , N. J. 1984 . “Classifying torsion-free subgroups of the Picard group” . Trans. Amer. Math. Soc. , 282 ( 1 ) : 205 – 235 . [Brunner et al. 1984]
   Web of Science ®Google Scholar
• Coxeter , H. S. M. and Whitrow , G. J. 1950 . “World-structure and non-Euclidean honeycombs” . Proc. Roy. Soc. London. Ser. A. , 201 : 417 – 437 . [Coxeter and Whitrow 1950]
   Web of Science ®Google Scholar
• Davis , M. W. 1985 . “A hyperbolic 4-manifold” . Proc. Amer. Math. Soc. , 93 ( 2 ) : 325 – 328 . [Davis 1985]
   Web of Science ®Google Scholar
• Pricke , R. 1891 . “Ueber eine besondere Classe discontinuirlicker Gruppen reeller linearer Substitutionen” . Math. Ann. , 38 : 50 – 81 . [Fricke 1891]
   Google Scholar
• Gibbons , G. W. 1996 . “Tunnelling with a negative cosmological constant” . Nuclear Phys. B , 472 ( 3 ) : 683 – 708 . [Gibbons 1996]
   Web of Science ®Google Scholar
• Gromov , M. 1982 . “Volume and bounded cohomology” . Publ. Math. Inst. Hautes Études Sci. , 56 : 5 – 99 . [Gromov 1982]
   Google Scholar
• Hantzsche , W. and Wendt , H. 1935 . “Dreidimensionale euklidische Raumformen” . Math. Ann. , 110 : 593 – 611 . [Hantzsche and Wendt 1935]
   Google Scholar
• Hilden , H. M. , Lozano , M. T. and Montesinos-Amilibia , J. M. 1992 . “On the Borromean orbifolds: geometry and arithmetic”. ” . In Topology ‘90 (Columbus, OH, 1990) Edited by: Apanasov , B. 133 – 167 . Berlin : de Gruyter. . [Hilden et al. 1992]
   Google Scholar
• Hopf , H. 1926 . “Über die curvatura integra Clifford-Kleinscher Raumformen” . Nachr. Ges. Wiss. Gottingen Math.-Phys. Kl. , : 131 – 141 . [Hopf 1926]
   Google Scholar
• Milnor , J. 1982 . “Hyperbolic geometry: the first 150 years” . Bull. Amer. Math. Soc. (N.S.) , 6 ( 1 ) : 9 – 24 . [Milnor 1982]
   Web of Science ®Google Scholar
• Newman , M. 1972 . Integral matrices New York : Academic Press. . [Newman 1972], Pure and Applied Mathematics 45
   Google Scholar
• Ratcliffe , J. G. 1994 . Foundations of hyperbolic manifolds New York : Springer. . [Ratcliffe 1994], Graduate Texts in Math. 149
   Google Scholar
• Ratcliffe , J. G. and Tschantz , S. T. 1998 . “Gravitational instantons of constant curvature” . Classical Quantum Gravity , 15 ( 9 ) : 2613 – 2627 . [Ratcliffe and Tschantz 1998]
   Web of Science ®Google Scholar
• Thurston , W. P. 1979 . “The geometry and topology of 3-manifolds” Princeton University. . [Thurston 1979], Technical report, Available at http://www.msri.org/publications/books/gt3m
   Google Scholar
• Thurston , W. P. 1997 . Three-dimensional geometry and topology vol. 1 , Princeton , NJ : Princeton University Press. . [Thurston 1997], Princeton Math. Series 35
   Google Scholar
• Vinberg , E. B. 1967 . “Discrete groups generated by reflections in Lobachevskii spaces” . Mat. Sb. (N.S.) , 72 : 471 – 488 . [Vinberg 1967], Correction in 73 (1967), 303. In Russian; translated in Math. USSR Sbornik 1(1967), 429–444
   Google Scholar
• Wang , H. C. 1972 . “Topics on totally discontinuous groups”. ” . In Symmetric spaces (St. Louis, MO, 1969–1970) Edited by: Boothby , W. M. and Weiss , G. L. 459 – 487 . New York : Marcel Dekker. . [Wang 1972], Pure and Appl. Math. 8
   Google Scholar
• Wielenberg , N. 1978 . “The structure of certain subgroups of the Picard group” . Math. Proc. Cambridge Philos. Soc. , 84 ( 3 ) : 427 – 436 . [Wielenberg 1978]
   Google Scholar
• Zimmermann , B. 1990 . “On the Hantzsche–Wendt manifold” . Monatshefte Math. , 110 ( 3–4 ) : 321 – 327 . [Zimmermann 1990]
   Web of Science ®Google Scholar