Hopf Fibration and Its Applications

  • M. Monastyrsky
Part of the Biological and Medical Physics, Biomedical Engineering book series (BIOMEDICAL)


Minimal Surface Cohomology Class Intersection Number Homotopy Group Closed Curf 
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  1. 1.
    B. Dubrovin, S. Novikov, A. Fomenko. Modern Geometry, I, II, III (Springer, New York 1984-1990)Google Scholar
  2. 2.
    M. Monastyrsky, Topology of Gauge Fields and Condensed Matter (Plenum, New York, 1993)zbMATHGoogle Scholar
  3. 3.
    J. H. C. Whitehead, Proc. Nat. Acad. Sci. USA, 117-123 (1947)Google Scholar
  4. 4.
    H. Whitney, Geometric Integration theory (Princeton University Press, Princeton, 1957)zbMATHGoogle Scholar
  5. 5.
    M. Monastyrsky, V. Retakh, Commun. Math. Phys. 103, 445-459, (1986)CrossRefMathSciNetADSGoogle Scholar
  6. 6.
    J. White, Geometry and topology of DNA-protein interactions, in New Scientific Applications of Geometry and Topology, ed. by De Witt, L. Sumners, Proc. of Symposia in Applied Math. N 45 (AMS, Providence 1992)Google Scholar
  7. 7.
    G. Cǎlugǎreanu, Czechoslovak Math. J. 11, 588-625 (1961)MathSciNetGoogle Scholar
  8. 8.
    H. H. Moffatt, R. L. Ricca, Proc. R. Soc. London A439, 411-429 (1992)MathSciNetADSGoogle Scholar
  9. 9.
    S. A. Safran Statistical Thermodynamics of Surfaces, Interfaces, and Membrans (Addison-Wesley, Reading, 2003)Google Scholar
  10. 10.
    E. I. Kats, M. I. Monastyrsky, JETP, 91, 1279-1285 (2000)CrossRefADSGoogle Scholar
  11. 11.
    W. Blaschke, G. Thomsen, Vorlesungen über Differential geometry III (Springer, Berlin Heidelberg New York, 1925)Google Scholar
  12. 12.
    U. Pinkal, Invent. Math. 81, 379-386 (1985)CrossRefMathSciNetADSGoogle Scholar
  13. 13.
    J. Langer, D. Singer, Bull. London Math. Soc. 16, 531-534 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    S. P. Novikov, Russ. Math. Survey, 37, (N5), 349 (1982)CrossRefGoogle Scholar
  15. 15.
    S. P. Novikov, Russ. Math. Survey, 39, (N5), 17-106 (1984)CrossRefGoogle Scholar
  16. 16.
    E. Witten, Commun. Math. Phys. 92, 455-472 (1984)zbMATHCrossRefMathSciNetADSGoogle Scholar
  17. 17.
    F. Wilczek, Fractional Statistics and Anyon Superconductivity (World Scientific, Singapure, 1990)Google Scholar
  18. 18.
    R. G. Muf (J. Frölich et al. ) The Fractional Quantum Hall effect, Chern-Simons theory, and Integral lattice, Proceedings of International Congress of Mathe-maticians, (Zürich, Birkhäuser, Basel, 1995)Google Scholar
  19. 19.
    M. I. Monastyrsky, P. V. Sasorov, Sov. Phys. JETP 66(4), 683-688 (1987)Google Scholar
  20. 20.
    V. I. Arnold, B. A. Khesin. Topological Methods in Hydrodynamics, (Springer, Berlin Heidelberg New York, 1998)zbMATHGoogle Scholar
  21. 21.
    L. Faddeev, A. J. Niemi, Toroidal configurations as stable solitons, hep-th 9705176 (22. 05. 1997)Google Scholar
  22. 22.
    F. B. Fuller, Proc. Nat. Acad. Sci. USA 75, 3557 (1978)zbMATHCrossRefMathSciNetADSGoogle Scholar
  23. 23.
    J. White, Amer. J. Math. 91, 693-728 (1969)zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    M. F. Atiyah, The geometry and physics of knots (Cambridge University Press, Cambridge, 1990)zbMATHCrossRefGoogle Scholar
  25. 25.
    R. Mosseri, Two and three qubits geometry and Hopf fibrations, (in Topology and Condensed matter, ed. by M. Monastyrsky (Springer, Berlin Heidelberg New York 2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • M. Monastyrsky
    • 1
  1. 1.Institute of Theoretical and Experimental PhysicsMoscowRussia

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