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Über Konvergenz von Spektralfolgen der stabilen Homotopietheorie

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Abstract

We discuss the problem of convergence of spectral sequences that arise from a filtration of a spectrum in Boardman's stable homotopy category by applying a generalized homology, “homotopy” or cohomology theory. The criteria we get give e.g. the convergence of the Adams spectral sequence for a generalized homology theory in certain cases (using similar methods this equestion has been considered independently by J. F. Adams in his forthcoming Chicago lecture notes), and some results on the Adams cohomology spectral sequence including the well-known convergence properties in case of singular cohomology with Zp-coefficients and complex cobordism.

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Literatur

  1. ADAMS, J.F.: On the structure and applications of the Steenrod algebra. Comment. Math. Helv. 32, 180–214 (1958)

    Google Scholar 

  2. ADAMS, J.F.: Lectures on generalized cohomology. Lecture Notes in Math. 99, 1–138, Springer (1969).

  3. ADAMS, J.F.: Algebraic topology in the last decade. Lecture Notes Summer Institute on Algebraic Topology, Wisconsin (1970).

  4. ATIYAH, M.F.: Characters and cohomology of finite groups. Publ. Inst. Hautes Etudes Sci. No. 9, 23–64 (1961).

    Google Scholar 

  5. BAAS, N.A.: A theorem concerning the convergence of the Adams spectral sequences. Preprint Series No. 26. Matematisk Institut, Aarhus (1968/69).

    Google Scholar 

  6. BAAS, N.A.: On the stable Adams spectral sequences. Various Publication Series No. 6. Matematisk Institut, Aarhus (1969).

    Google Scholar 

  7. BOARDMAN, J.M.: Stable homotopy theory. University of Warwick (1965). (vervielfältigt)

  8. BOARDMAN, J.M.: Stable homotopy theory, Chap. I, II, Appendix B. The Johns Hopkins University (1969/70). (vervielfältigt)

  9. BRÖCKER, Th. and tom DIECK, T.: Kobordismentheorie. Lecture Notes in Math. 178, Springer (1970).

  10. CARTAN, H. und EILENBERG, S.: Homological Algebra, Princeton University Press (1956).

  11. CONNER, P.E. und SMITH, L.: On the complex bordism of finite complexes. Publ. Inst. Haute Etudes Sci. No. 37, 417–521 (1969).

    Google Scholar 

  12. DOLD, A.: On general cohomology. Lectures at Nordic Summer School, Matematisk Institut Aarhus (1968).

  13. HU, S. T.: Homotopy Theory, Academic Press New York (1959).

  14. MISHCHENKO, A.S.: Spectral sequences of Adams type. Math. Notes 1 (1967), 226–230 (1968). (engl. Übersetzung).

    Google Scholar 

  15. NOVIKOV, S.P.: The methods of algebraic topology from the viewpoint of cobordism theories. Izv. Akad. Nauk S.S.S.R. Ser. Mat. 31, 855–951 (1967).

    Google Scholar 

  16. SERRE, J. P.: Groupes d'Homotopie et Classes de Groupes Abéliens. Ann. of Math. 58, 258–294 (1953).

    Google Scholar 

  17. VOGT, R.: Boardman's stable homotopy category. Lecture Notes Series No. 21, Matematisk Institut, Aarhus (1970).

    Google Scholar 

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  1. Mathematisches Institut der Universität, Im Neuenheimer Feld 9, 69, Heidelberg

    Volker Puppe

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  1. Volker Puppe
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Puppe, V. Über Konvergenz von Spektralfolgen der stabilen Homotopietheorie. Manuscripta Math 6, 327–358 (1972). https://doi.org/10.1007/BF01303687

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  • DOI: https://doi.org/10.1007/BF01303687

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