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Rationale Homotopietypen

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Abstract

We call a CW-complex unstable, if all attaching maps vanish under suspension. For a one-connected CW-space X we construct a unstable CW-complex ¯X and a mapping ¯X→X, which is a rational homotopy equivalence. As an application we imbed the rational Hurewicz-homomorphism into an exact sequence.

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Literaturverzeichnis

  1. ADAMS, J.F., HILTON, P.J.: On the chain algebra of a loop space. Comment. math. Helvet.20, 305–330 (1955).

    Google Scholar 

  2. BAUES, H.J.: Iterierte Join-Konstruktionen. Math. Z.131, 77–84 (1973).

    Google Scholar 

  3. BAUES, H.J.: Relative Homotopiegruppen bei Abbildungs kegeln. Comp. Math.32 2, 169–183 (1976).

    Google Scholar 

  4. BAUES, H.J., LEMAIRE, J.M.: Minimal models in homotopy theory, erscheint in Math. Ann.

  5. BERSTEIN, I.: Homotopy mod C of spaces of category 2. Comment. Math. Helv.35, 9–14 (1961).

    Google Scholar 

  6. BOTT, R., SAMELSON, H.: On the Pontryagin product in spaces of paths. Comment. Math. Helv.27, 320–337 (1953).

    Google Scholar 

  7. CURJEL, C.R.: A note on spaces of category ≤2. Math. Z.80, 293–299 (1963).

    Google Scholar 

  8. DYER, M.: Rational homology and Whitehead products. Pac. J. Math.40, (1), 59–71 (1972).

    Google Scholar 

  9. FRIEDLANDER, E., GRIFFITHS, P.A., MORGAN, J.: Homotopy theory and differential forms. Seminario di Geometria 1972, Consiglio Nazionale delle Richerche Centro di Annalisi Globale. Firence.

  10. HILTON, P.J.: On the homotopy groups of a union of spheres. J. London Math. Soc.30, 154–172 (1955).

    Google Scholar 

  11. MILNOR, J., MOORE, J.C.: On the structure of Hopf algebras. Ann. Math.81, 211–264 (1965).

    Google Scholar 

  12. QUILLEN, D.: Rational homotopy theory. Ann. Math.90, 205–295 (1969).

    Google Scholar 

  13. RUTTER, J.W.: The suspension of the loops on a space with comultiplication. Math. Ann.209, 69–82 (1974).

    Google Scholar 

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Authors and Affiliations

  1. Sonderforschungsbereich 40 ‘Theoretische Mathematik’, Mathematisches Institut der Universität, Wegelerstr. 10, D-5300, Bonn, Bundesrepublik Deutschland

    Hans Joachim Baues

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  1. Hans Joachim Baues
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†Der Autor wurde von der ‘CNRS’ Frankreich unterstützt.

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Baues, H.J. Rationale Homotopietypen. Manuscripta Math 20, 119–131 (1977). https://doi.org/10.1007/BF01170720

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  • DOI: https://doi.org/10.1007/BF01170720

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