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Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 2, Pages 413–424 (Mi izv1484)  

This article is cited in 16 scientific papers (total in 17 papers)

The absence of discrete reflection groups with noncompact fundamental polyhedron of finite volume in Lobachevskii space of large dimension

M. N. Prokhorov


Abstract: The following theorem is proved: There are no discrete groups generated by reflections with fundamental polyhedron of finite volume in Lobachevskii space of dimension $995$.
Bibliography: 8 titles.

Full text: PDF file (1387 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1987, 28:2, 401–411

Bibliographic databases:

UDC: 512
MSC: Primary 51F15; Secondary 20H15, 22E40, 51M10, 51M20, 52A25

Citation: M. N. Prokhorov, “The absence of discrete reflection groups with noncompact fundamental polyhedron of finite volume in Lobachevskii space of large dimension”, Izv. Akad. Nauk SSSR Ser. Mat., 50:2 (1986), 413–424; Math. USSR-Izv., 28:2 (1987), 401–411

Citation in format AMSBIB
\Bibitem{Pro86}
\by M.~N.~Prokhorov
\paper The absence of discrete reflection groups with noncompact fundamental polyhedron of finite volume in Lobachevskii space of large dimension
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 2
\pages 413--424
\mathnet{http://mi.mathnet.ru/izv1484}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=842588}
\zmath{https://zbmath.org/?q=an:0613.51010|0604.51007}
\transl
\jour Math. USSR-Izv.
\yr 1987
\vol 28
\issue 2
\pages 401--411
\crossref{https://doi.org/10.1070/IM1987v028n02ABEH000889}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. G. Khovanskii, “Hyperplane sections of polyhedra, toroidal manifolds, and discrete groups in Lobachevskii space”, Funct. Anal. Appl., 20:1 (1986), 41–50  mathnet  crossref  mathscinet  zmath  isi
    2. V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities. II”, Math. USSR-Izv., 33:2 (1989), 355–372  mathnet  crossref  mathscinet  zmath
    3. V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities. III”, Math. USSR-Izv., 35:3 (1990), 657–675  mathnet  crossref  mathscinet  zmath
    4. V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities”, Math. USSR-Sb., 66:1 (1990), 231–248  mathnet  crossref  mathscinet  zmath  isi
    5. V. V. Nikulin, “Algebraic three-folds and the diagram method”, Math. USSR-Izv., 37:1 (1991), 157–189  mathnet  crossref  mathscinet  zmath  adsnasa
    6. V. V. Nikulin, “Reflection groups in Lobachevskii spaces and the denominator identity for Lorentzian Kac–Moody algebras”, Izv. Math., 60:2 (1996), 305–334  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. V. O. Bugaenko, “Klassifikatsiya mnogogrannikov Kokstera”, Matem. prosv., ser. 3, 7, MTsNMO, M., 2003, 82–106  mathnet
    8. P. V. Tumarkin, “Hyperbolic $n$-dimensional Coxeter polytopes with $n+3$ facets”, Russian Math. Surveys, 58:4 (2003), 805–806  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    9. Agol, I, “Finiteness of arithmetic hyperbolic reflection groups”, Groups Geometry and Dynamics, 2:4 (2008), 481  isi
    10. Anna Felikson, Pavel Tumarkin, “On hyperbolic Coxeter polytopes with mutually intersecting facets”, Journal of Combinatorial Theory, Series A, 115:1 (2008), 121  crossref
    11. P. V. Tumarkin, A. A. Felikson, “On simple ideal hyperbolic Coxeter polytopes”, Izv. Math., 72:1 (2008), 113–126  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    12. Maclachlan C., “Commensurability classes of discrete arithmetic hyperbolic groups”, Groups Geom Dyn, 5:4 (2011), 767–785  isi
    13. Guglielmetti R., “CoxIter – Computing invariants of hyperbolic Coxeter groups”, LMS J. Comput. Math., 18:1 (2015), 754–773  crossref  mathscinet  zmath  isi  elib  scopus
    14. Belolipetsky M., “Arithmetic hyperbolic reflection groups”, Bull. Amer. Math. Soc., 53:3 (2016), 437–475  crossref  mathscinet  zmath  isi  elib  scopus
    15. A. Yu. Vesnin, “Right-angled polyhedra and hyperbolic 3-manifolds”, Russian Math. Surveys, 72:2 (2017), 335–374  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    16. Turkalj I., “Reflective Lorentzian Lattices of Signature (5,1)”, J. Algebra, 513 (2018), 516–544  crossref  mathscinet  zmath  isi  scopus
    17. Kontorovich A. Nakamura K., “Geometry and Arithmetic of Crystallographic Sphere Packings”, Proc. Natl. Acad. Sci. U. S. A., 116:2 (2019), 436–441  crossref  isi  scopus
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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