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Methods of topological obstruction theory in condensed matter physics

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Abstract

The notion of relative topological textures — nonuniform states of the general type in condensed (ordered) media — is introduced. For the classification of such states, an effective method is proposed which is based on the topological obstruction theory. The examples of relative topological textures are examined within the framework of the approach studied here.

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References

  1. Mermin, N.D.: The topological theory of defects in ordered media. Rev. Mod. Phys.51, 591–648 (1979)

    Google Scholar 

  2. Michel, L.: Symmetry defects and broken symmetry. Configurations. Hidden symmetry. Rev. Mod. Phys.52, 617–651 (1980)

    Google Scholar 

  3. Mineev, V.P.: Topologically stable inhomogeneous states in ordered media. Sov. Sci. Rev. A2, 173–234 (1980)

    Google Scholar 

  4. Trebin, H.-R.: The topology of non-uniform media in condensed matter physics. Adv. Phys.31, 195–254 (1982)

    Google Scholar 

  5. Jaffe, A., Taubes, C.: Vortices and monopoles. Boston, Basel, Stuttgart: Birkhäuser 1980

    Google Scholar 

  6. Leinaas, J.M.: Topological charges in gauge theories. Fortschr. Phys.28, 579–631 (1980)

    Google Scholar 

  7. Konopleva, N.P., Popov, V.N.: Gauge fields. New York: Harwood 1981

    Google Scholar 

  8. Geometric techniques in gauge theories. Lecture Notes in Mathematics, Vol. 926. Berlin, Heidelberg, New York: Springer 1982

    Google Scholar 

  9. Mermin, N.D., Mineyev, V.P., Volovik, G.E.: Topological analysis of the cores of singularities in3He-A. J. Low Temp. Phys.33, 117–126 (1978)

    Google Scholar 

  10. Mineyev, V.P., Volovik, G.E.: Planar and linear solitons in superfluid3He. Phys. Rev. B18, 3197–3203 (1978)

    Google Scholar 

  11. Spanier, E.H.: Algebraic topology. New York, San Francisco, St. Louis, Toronto, London, Sydney: McGraw-Hill 1966

    Google Scholar 

  12. Hu, S.-T.: Homotopy theory. New York, London: Academic Press 1959

    Google Scholar 

  13. Dubrovin, B.A., Novikov, S.P., Fomenko, A.T.: Modern geometry: Methods of homology theory. Moscow: Nauka 1984 (in Russian)

    Google Scholar 

  14. Kleman, M., Michel, L.: Spontaneous breaking of euclidean invariance and classification of topology stable defects and configurations of crystals and liquid crystals. Phys. Rev. Lett.40, 1387–1390 (1978)

    Google Scholar 

  15. Physics of defects, Balian, R., Kleman, M., Poireir, J.-P. (eds.): Amsterdam, New York, Oxford: North-Holland 1981

    Google Scholar 

  16. Husemoller, D.: Fibre bundles. New York, St. Louis, San Francisco, Toronto, London, Sydney: McGraw-Hill 1966

    Google Scholar 

  17. Milnor, J.W., Stasheff, J.D.: Characteristic classes. Princeton, NJ: Princeton University Press and University of Tokyo Press 1974

    Google Scholar 

  18. Michenko, A.S.: Vector bundles and their applications. Moscow: Nauka 1984 (in Russian)

    Google Scholar 

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Communicated by J. Fröhlich

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Ovid'ko, I.A., Romanov, A.E. Methods of topological obstruction theory in condensed matter physics. Commun.Math. Phys. 105, 443–453 (1986). https://doi.org/10.1007/BF01205936

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  • DOI: https://doi.org/10.1007/BF01205936

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