Abstract
A complete classification of the height atoms whose symmetry groups act transitively on the vertices of atoms is obtained.
Similar content being viewed by others
References
A. V. Bolsinov and A. T. Fomenko, Integrable Hamiltonian Systems: Geometry, Topology, Classification (Izd. Udmurtskii Universitet, Izhevsk, 1999; CRC Press Company, Boca Raton, L., N.Y., Washington, D.C., 2004).
V. O. Manturov, “Bifurcations, Atoms and Knots,” Vestn. Mosk. Univ., Matem. Mekhan., No. 1, 3 (2000) [Moscow Univ. Math. Bulletin 55 (1), 1 (2000)].
A. T. Fomenko, “The Topology of Surfaces of Constant Energy in Integrable Hamiltonian Systems, and Obstructions to Integrability,” Izvestiya Akad. Nauk SSSR, Matem. 50 (6), 1276 (1986) [Math. of the USSR–Izvestiya 29 (3), 629 (1987)].
A. T. Fomenko, “Topological Invariants of Liouville Integrable Hamiltonian Systems,” Funk. Analiz. Prilozh. 22 (4), 38 (1988) [Funct. Analysis and Its Appl. 22 (4), 286 (1988)].
A. T. Fomenko, “The Symplectic Topology of Completely Integrable Hamiltonian Systems,” Uspekhi Matem. Nauk 44 (1), 145 (1989) [Russian Math. Surveys 44 (1), 181 (1989)].
A. T. Fomenko, “A Bordism Theory for Integrable Nondegenerate Hamiltonian Systems with Two Degrees of Freedom. A New Topological Invariant of Higher-Dimensional Integrable Systems,” Izvestiya Akad. Nauk SSSR, Matem. 55 (4), 747 (1990) [Math. of the USSR–Izvestiya 39 (1), 731 (1992)].
A. T. Fomenko, “A Topological Invariant which Roughly Classifies Integrable Strictly Nondegenerate Hamiltonians on Four-Dimensional Symplectic Manifolds,” Funk. Analiz. Prilozh. 25 (4), 23 (1991) [Funct. Analysis and Its Appl. 25 (4), 262 (1991)].
A. T. Fomenko and H. Zieschang, “A Topological Invariant and a Criterion for the Equivalence of Integrable Hamiltonian Systems with Two Degrees of Freedom,” Izvestiya Akad. Nauk SSSR, Matem. 54 (3), 546 (1990) [Math. of the USSR–Izvestiya 36 (3), 567 (1991)].
D. P. Ilyutko and V. O. Manturov, Virtual Knots: the State of the Art, Series on Knots and Everything. Vol. 51, (World Sci. Press, Singapore, 2012).
E. A. Kudryavtseva, I. M. Nikonov, and A. T. Fomenko, “Maximally Symmetric Cell Decompositions of Surfaces and Their Coverings,” Matem. Sbornik 199 (9), 3 (2008) [Sbornik: Math. 199 (9), 1263 (2008)].
E. A. Kudryavtseva, I. M. Nikonov, and A. T. Fomenko, “Symmetries and Irreducible Abstract Polyhedra,” in: Modern Problems of Mathematics and Mechanics, Ed. by A. T. Fomenko (Moscow State Univ., Moscow, 2009), pp. 58–97.
I. M. Nikonov and N. V. Volchanetskii, “Maximally Symmetric Height Atoms,” Vestn. Mosk. Univ., Matem. Mekhan., No. 2, 3 (2013) [Moscow Univ. Math. Bulletin 68 (2), 83 (2013)].
A. A. Oshemkov, “Morse Functions on Two-Dimensional Surfaces. Encoding Singularities,” Trudy Matem. Inst. RAN 205, 131 (1994) [Proc. of the Steklov Inst. of Math. 205, 119 (1995)].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © I.M. Nikonov, 2016, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2016, Vol. 71, No. 6, pp. 17–25.
About this article
Cite this article
Nikonov, I.M. Height atoms whose symmetry groups act transitively on their vertex sets. Moscow Univ. Math. Bull. 71, 233–241 (2016). https://doi.org/10.3103/S0027132216060036
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0027132216060036