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Etale homotopy theory and shape

Part of the Lecture Notes in Mathematics book series (LNM,volume 428)

Keywords

  • Homotopy Type
  • Homotopy Group
  • Algebraic Topology
  • Inverse Limit
  • Homotopy Theory

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References

  1. G. Allaud, On the classification of fiber spaces, Math. Zeitschr. 92, 110–125 (1966).

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. M. F. Atiyah and B. G. Segal, Equivariant K-theory and Completion, J. Diff. Geo. 3 (1969), 1–18.

    MathSciNet  MATH  Google Scholar 

  3. M. Artin and B. Mazur, Etale Homotopy, Lecture notes in Math. 100. Springer (1969).

    Google Scholar 

  4. K. Borsuk, Theory of Retracts, Monografie Matematyczne 44, Warzawa 1967.

    Google Scholar 

  5. _____, Concerning Homotopy Properties of Compacta, Fund. Math. 62 (1968), 223–254.

    MathSciNet  MATH  Google Scholar 

  6. _____, On movable compacta, Fund. Math. 66 (1969), 137–146.

    MathSciNet  MATH  Google Scholar 

  7. _____, Theory of Shape, Lecture Notes No. 28, Matematisk Inst., Aarhus Univ., 1971, 1–145.

    Google Scholar 

  8. A. K. Bousfield and D. M. Kan, Homotopy Limits, Completions and Localizations, Lecture notes in Math. 302 (1972).

    Google Scholar 

  9. T. A. Chapman, On some applications of infinite dimensional manifolds to the theory of shape, (to appear).

    Google Scholar 

  10. J. Cohen, The homotopy groups of inverse limits, Proceedings of the London Math. So., Vol. XXVII, July, 1973, 159–192.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. D. A. Edwards and R. Geoghegan, Compacta weak shape equivalent to ANR's, (to appear in Fund. Math.)

    Google Scholar 

  12. _____ and P. McAuley, Pro-fibrations, shape and classification, (in preparation).

    Google Scholar 

  13. R. H. Fox, A quick trip through Knot Theory, in Topology of 3-Manifolds, ed. M. K. Fort, Jr., Prentice-Hall Inc., Englewood Cliffs, N. J., 1962.

    Google Scholar 

  14. _____, On Shape, Fund. Math. LXXIV (1972), 47–71.

    MATH  Google Scholar 

  15. E. Friedlander, Fibrations in Etale Homotopy Theory, to appear.

    Google Scholar 

  16. _____, The Etale Homotopy Theory of a Geometric Fibration, to appear.

    Google Scholar 

  17. R. Geoghegan and R. Summerhill, Concerning the shapes of finite dimensional compacta, Trans. Amer. Math. Soc. 179 (1973), 281–292.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. M. Greenberg, Lectures on Algebraic Topology, Benjamin, Amsterdam, 1967.

    MATH  Google Scholar 

  19. A. Grothendieck, Technique de descente et theorems d'existence en geometrie algebrique II, Seminar Bourbaki, 12 iene annee, 1959–60, exp. 195.

    Google Scholar 

  20. D. Handel and J. Segal, An acyclic continuum with non-movable suspensions, (to appear).

    Google Scholar 

  21. _____, Finite Shape Classifications, (to appear).

    Google Scholar 

  22. D. Husemoller, Fibre Bundles, McGraw-Hill Book Company, 1966.

    Google Scholar 

  23. J. Keesling, Continuous Functions induced by Shape Morphisms, to appear.

    Google Scholar 

  24. D. Knutson, Algebraic Spaces, Lecture notes in Math. 203, Springer (1971).

    Google Scholar 

  25. J. Levan, Shape Theory, Thesis 1973 (unpublished).

    Google Scholar 

  26. A. Lundell and S. Weingram, The topology of CW complexes, Van Nostrand Reinhold Company (1969).

    Google Scholar 

  27. I. G. MacDonald, Algebraic Geometry — Introduction to Schemes, W. A. Benjamin, Inc., 1968.

    Google Scholar 

  28. S. Mardesic, n-dimensional LC n−1 compacta are movable, Bull. Acad. Polon. Sci. Sec. Sci. Math. Astr. Phys. (1971), 505–509.

    Google Scholar 

  29. _____, Shapes for topological spaces, to appear.

    Google Scholar 

  30. _____, A survey of the shape theory of compacta, to appear.

    Google Scholar 

  31. _____ and J. Segal, Shapes of compacta and ANR — systems, Fund. Math. LXXII, (1971), 41–59.

    MathSciNet  MATH  Google Scholar 

  32. M. Moszynska, The Whitehead Theorem in the Theory of Shapes, to appear in Fund. Math.

    Google Scholar 

  33. L. Pontrjagin, Topological Groups, Princeton University Press, 1946.

    Google Scholar 

  34. T. Porter, Cech Homotopy I, J. London Math. Soc. (2), 6 (1973) 429–436.

    CrossRef  MathSciNet  MATH  Google Scholar 

  35. D. Quillen, Some remarks on étale homotopy theory and a conjecture of Adams, Topology 7 (1968) 111–116.

    CrossRef  MathSciNet  MATH  Google Scholar 

  36. J. P. Serre, Groupes d'homotopie et classes de groupes abeliene, Annals of Math., Vol. 58, (1953), 258–294.

    CrossRef  MATH  Google Scholar 

  37. E. Spanier, Algebraic Topology, McGraw-Hill, 1967.

    Google Scholar 

  38. D. Sullivan, Geometric Topology, Part I, Localization, Periodicity and Galois Symmetry, Mimeographed Notes M.I.T. 1970.

    Google Scholar 

  39. A. Dold, Lectures on Algebraic Topology, Springer-Verlag, New York, 1972.

    CrossRef  MATH  Google Scholar 

  40. C. H. Dowker, Homology of Relations, Ann. of Math, 56 (1952), 84–95.

    CrossRef  MathSciNet  MATH  Google Scholar 

  41. S. Eilenberg and N. Steenrod, Foundations of Algebraic Topology, Princeton University Press, Princeton, New Jersey (1952).

    CrossRef  MATH  Google Scholar 

  42. W. Scheffer, Maps between topological groups that are homotopic to homomorphism, Proc. Amer. Math. Soc. 33 (1972), 562–567.

    CrossRef  MathSciNet  MATH  Google Scholar 

  43. J. Stasheff, H-spaces from a homotopy point of view, Lecture notes in Mathematics 161, Springer (1970).

    Google Scholar 

  44. R. Overton, Cèch homology for movable compacta, to appear in Fund. Math.

    Google Scholar 

  45. K. Kuperberg, An isomorphism theorem of Hurewicz type in Borsuk's theory of shape, to appear.

    Google Scholar 

  46. N. Steenrod, The topology of fibre bundles, Princeton University Press (1951).

    Google Scholar 

  47. D. S. Kahn, An example in Cèch cohomology, Proc. Amer. Math. Soc. 16 (1965), 584.

    MathSciNet  MATH  Google Scholar 

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© 1974 Springer-Verlag

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Edwards, D.A. (1974). Etale homotopy theory and shape. In: McAuley, L.F. (eds) Algebraic and Geometrical Methods in Topology. Lecture Notes in Mathematics, vol 428. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0070535

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  • DOI: https://doi.org/10.1007/BFb0070535

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  • Print ISBN: 978-3-540-07019-1

  • Online ISBN: 978-3-540-37300-1

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