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Realisierung formaler Gruppen durch Kohomologiefunktoren

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Abstract

To any multiplicative cohomology theory h with the property that complex line bundles are h-oriented corresponds a formal group law F(X,Y) over the ring h(pt) which describes the Euler class of a tensor product of line bundles by means of the Euler classes of its factors. We consider this formal group as an invariant of h and give sufficient conditions under which a morphism between formal groups of cohomology theories h,k can be extended in one and only one way to a transformation of theories h→k. Some typical applications will be discussed.

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Literatur

  1. ADAMS,J.F.: Quillen's work on formal groups and complex cobordism. University of Chicago lectures (1970).

  2. ADAMS,J.F.: Stable homotopy and generalised homology. University of Chicago lectures (1971).

  3. ADAMS,J.F.: Lectures on generalised cohomology. Springer lecture notes 99 (1969).

  4. ARAKI, S., TODA, H.: Multiplications in mod q cohomology theories. Osaka Journ. Math.2, 71–115 (1965).

    Google Scholar 

  5. BAAS, N.A.: On bordism theory of manifolds with singularities. Math. Scand.33, 279–302 (1973).

    Google Scholar 

  6. BAAS,N.A.: Bordism theories with singularities.Proc. Adv. Study Inst. Alg. Topology Aarhus, 1–16(1970).

  7. DOLD,A.: Lectures on general cohomology. Mimeographed notes, Aarhus (1968).

  8. DOLD,A.: Chern classes in general cohomology. Symposia Mathematica vol. V (1970).

  9. FROEHLICH,A.: Formal groups. Springer lecture notes 74.

  10. KAPLANSKY,I.: Commutative rings. Allyn and Bacon, Boston (1970).

    Google Scholar 

  11. PUPPE,D.: On the stable homotopy category. Preprint Univ. Heidelberg (1972).

    Google Scholar 

  12. QUILLEN,D.: Elementary proofs of some results of cobordism theory using Steenrod operations. Advances in Math.7, 28–56 (1971).

    Google Scholar 

  13. SULLIVAN,D.: On the Hauptvermutung for manifolds. Bull. A.M.S.73, 598–600 (1967).

    Google Scholar 

  14. VOGT,R.: Boardmans stable homotopy category. Mimeographed notes, Aarhus Univ. (1970).

  15. WUERGLER,U.: Ueber Kohomologietheorien mit formaler Gruppe der Charakteristik p. Comm. Math. Helv.48, 531–536 (1973).

    Google Scholar 

  16. WUERGLER,U.: Cohomologie et groupes formels. C.R.Acad. Sc. Paris278, 981–983 (1974).

    Google Scholar 

  17. YOSIMURA,Z.: On cohomology theories of infinite CW-complexes. Publ. RIMS Kyoto Univ.8, 295–310 (1972/73).

    Google Scholar 

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  1. Math. Inst. der Univ., Sidlerstrasse 5, CH-3000, Bern

    Urs Würgler

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  1. Urs Würgler
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Würgler, U. Realisierung formaler Gruppen durch Kohomologiefunktoren. Manuscripta Math 14, 65–87 (1974). https://doi.org/10.1007/BF01637623

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  • DOI: https://doi.org/10.1007/BF01637623

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