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Shape theory of compact transformation groups

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Abstract

In this paper, we present a systematic investigation of shape theory of compact transformation groups, the so-called equivariant shape theory.

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References

  1. S. Antonian, “Equivariant embeddings into G-ARs,” Glas. Mat. Ser. III, 22 (42), No. 2, 503–533 (1987).

    MathSciNet  Google Scholar 

  2. V. Baladze, “Fiber shape theory,” Rend. Inst. Mat. Univ. Trieste, 22, Nos. 1-2, 67–77 (1990).

    MathSciNet  MATH  Google Scholar 

  3. V. Baladze, Resolutions of spaces and continuous maps and their applications in spectral homotopy theory, Dissertation, Tbilisi (1993).

  4. A. Beridze, “On shape theory with compact supports for pairs of spaces,” in: Abstracts Int. Math. Congress, Zagreb (2002).

  5. K. Borsuk, “Concerning homotopy properties of compacta,” Fund. Math., 62, 223–254 (1968).

    MathSciNet  MATH  Google Scholar 

  6. K. Borsuk, “Fundamental retracts and extensions of fundamental sequences,” Fund. Math., 64, 55–85 (1969); errata, Fund. Math., 64, 375 (1969).

    MATH  Google Scholar 

  7. K. Borsuk, “On the concept of shape for metrizable spaces,” Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys., 18, 127–132 (1970).

    MathSciNet  MATH  Google Scholar 

  8. M. Dzadzamia, “Equivariant shape for G-pairs. Bull. Georgian Acad. Sci., 162, No. 1, 18–21 (2000).

    MathSciNet  MATH  Google Scholar 

  9. M. Dzadzamia, “On equivariant shape retracts,” Bull. Georgian Acad. Sci., 165, No. 2, 247–250 (2002).

    MathSciNet  MATH  Google Scholar 

  10. M. Dzadzamia, “On the equivariant shape theory with compact invariant supports,” Bull. Georgian Acad. Sci. 166, No. 2, 242–246 (2002).

    MathSciNet  MATH  Google Scholar 

  11. R. H. Fox, “On shape,” Fund. Math., 74, No. 1, 47–71 (1972).

    MathSciNet  MATH  Google Scholar 

  12. S. Mardešić, “Retracts in shape theory,” Glasnik Mat. Ser. III, 6 (26), 153–163 (1971).

    MathSciNet  Google Scholar 

  13. S. Mardešić, “Approximate polyhedra, resolutions of maps and shape fibrations,” Fund. Math., 114, No. 1, 53–78 (1981).

    MathSciNet  MATH  Google Scholar 

  14. I. Pop, “An equivariant shape theory,” Ann. Stiint. Univ. Al. I. Cuza Iasi Sect. I a Mat., 30, No. 2, 53–67 (1984).

    MATH  Google Scholar 

  15. Yu. M. Smirnov, “Some topological aspects of the theory of topological transformation groups,” in: General Topology and Its Relations to Modern Analysis and Algebra, IV. Proc. Fourth Prague Topological Symp., Prague, 1976. Lect. Notes Math., 609, Springer-Verlag, Berlin (1977), pp. 196–204.

    Chapter  Google Scholar 

  16. Yu. M. Smirnov, “Shape theory and continuous transformation groups,” Usp. Mat. Nauk, 34, No. 6 (210), 119–123 (1979).

  17. Yu. M. Smirnov, “Shape theory for G-pairs,” Usp. Mat. Nauk, 40, No. 2 (242), 151–165 (1985).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Shota Rustaveli State University, Batumi, Georgia

    M. Dzadzamia

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  1. M. Dzadzamia
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Correspondence to M. Dzadzamia.

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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 74, Proceedings of the International Conference “Modern Algebra and Its Applications” (Batumi, 2010), Part 1, 2011.

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Dzadzamia, M. Shape theory of compact transformation groups. J Math Sci 186, 726–740 (2012). https://doi.org/10.1007/s10958-012-1024-8

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