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The equivariant Künneth theorem in K-theorem

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Topics in K-Theory

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Introduction-bibliography

  1. L. Hodgkin, An Equivariant Künneth formula for K-theory, preprint, University of Warwick, 1967.

    Google Scholar 

  2. J.F. Adams, Lectures on Generalized Cohomology, in ‘Category Theory Homology Theory and Applications', Lecture Notes in Math. 99, Springer, 1969.

    Google Scholar 

  3. J.F. Adams, On the Cobar construction, Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 409–412.

    Article  MathSciNet  MATH  Google Scholar 

  4. D.W. Anderson and L.H. Hodgkin, The K-theory of Eilenberg-MacLane complexes, Topology 7 (1968), 317–329.

    Article  MathSciNet  MATH  Google Scholar 

  5. S. Araki, Hopf Structures attached to K-theory: Hodgkin's Theorem, Ann. Math. 85 (1967), 508–525.

    Article  MathSciNet  MATH  Google Scholar 

  6. M.F. Atiyah, Vector bundles and the Künneth formula, Topology. 1 (1962), 245–248.

    Article  MathSciNet  MATH  Google Scholar 

  7. -, Bott periodicity and the index of elliptic operators, Quart. J. Math. 19 (1968), 113–140

    Article  MathSciNet  MATH  Google Scholar 

  8. -, Characters and cohomology of finite groups, Publ. Math. IHES 9 (1961), 23–64.

    Article  MathSciNet  MATH  Google Scholar 

  9. M.F. Atiyah and F. Hirzebruch, Vector bundles and homogeneous spaces, Proc. Sympos. Pure Math. AMS 3 (1961), 7–38.

    Article  MathSciNet  MATH  Google Scholar 

  10. M.F. Atiyah and G. Segal, Equivariant K-theory and completion, J. Diff. Geom. 3 (1969), 1–19.

    MathSciNet  MATH  Google Scholar 

  11. J. Beck, On H-spaces and infinite loop spaces, in ‘Category Theory, Homology Theory and Applications, Lecture Notes in Math. 99, Springer, 1969.

    Google Scholar 

  12. R. Bott, The Stable Homotopy of the Classical Groups, Ann. Math. 70 (1959), 313–337.

    Article  MathSciNet  MATH  Google Scholar 

  13. S. Eilenberg and J.C. Moore, Homology and Fibrations I, Comm. Math. Helv. 40 (1966), 199–236.

    Article  MathSciNet  MATH  Google Scholar 

  14. L Hodgkin, The K-theory of Lie groups, Topology 6 (1967), 1–36.

    Article  MathSciNet  MATH  Google Scholar 

  15. J.P. May, The cohomology of principal bundles, homogeneous spaces and 2-stage Postnikov systems, Bull. A.M.S. 74 (1968), 334–339.

    Article  MathSciNet  MATH  Google Scholar 

  16. J. McLeod (to appear).

    Google Scholar 

  17. H. Minami, A Künneth formula for equivariant K-theory, Osaka J. Math. 6 (1969), 143–6.

    MathSciNet  MATH  Google Scholar 

  18. H. Pittie, Homogeneous vector bundles on homogeneous spaces, Topology 11 (1972), 199–204.

    Article  MathSciNet  MATH  Google Scholar 

  19. D.L. Rector, Steenrod operations in the Eilenberg-Moore spectral sequence, Comm. Math. Helv. 45 (1970), 540–552.

    Article  MathSciNet  MATH  Google Scholar 

  20. A. Roux, Application de la suite spectrale d'Hodgkin aux variétés de Stiefel, Bull. Soc. Math. France 99 (1971), 345–368.

    MathSciNet  MATH  Google Scholar 

  21. G. Segal, Equivariant K-theory, Publ. Math. THES 34 (1968), 129–151.

    Article  MathSciNet  MATH  Google Scholar 

  22. L. Smith, Lectures on the Eilenberg-Moore spectral sequence, Lecture Notes in Math. no. 134 (1970), Springer.

    Google Scholar 

  23. V.P. Snaith, On the Künneth formula spectral sequence in equivariant K-theory, Proc. Camb. Phil. Soc. 72 (1972), 167–177.

    Article  MathSciNet  MATH  Google Scholar 

  24. -, Massey products in K-theory, Proc. Camb. Phil. Soc. 68 (1970), 303–320.

    Article  MathSciNet  MATH  Google Scholar 

  25. -, Massy products in K-theory II, Proc. Camb. Phil. Soc. 69 (1971), 259–289.

    Article  MathSciNet  MATH  Google Scholar 

  26. V.P. Snaith, On the K-theory of homogeneous spaces and conjugate bundles of Lie groups, Proc. L.M.S. (III) 22 (1971), 562–584.

    Article  MathSciNet  MATH  Google Scholar 

Part I Bibliography

  1. D.W. Anderson and L. Hodgkin, The K-theory of Eilenberg-MacLane complexes, Topology 7 (1968), 317–329.

    Article  MathSciNet  MATH  Google Scholar 

  2. M.F. Atiyah, Characters and cohomology of finite groups, Publ. Math. I H E S 9 (1961), 23–64.

    Article  MathSciNet  MATH  Google Scholar 

  3. -, Vector bundles and the Künneth formula, Topology 1 (1962), 245–248.

    Article  MathSciNet  MATH  Google Scholar 

  4. M.F. Atiyah, K-theory, Benjamin, 1967.

    Google Scholar 

  5. J. Beck, On H-spaces and infinite loop spaces. Category Theory, Homology Theory and their Applications III, Lecture Notes in Mathematics no. 99, Springer, 1969.

    Google Scholar 

  6. A. Borel et al., Seminar on Transformation Groups, Princeton, Ann. of Math. Studies no. 46, 1960.

    Google Scholar 

  7. G. Bredon, Equivariant cohomology theories, Lecture Notes in Mathematics no. 34, Springer 1967.

    Google Scholar 

  8. H. Cartan, Séminaire de l'E.N.S. no. 11 (1958–9), Invariant de Hopf.

    Google Scholar 

  9. H. Cartan, and S. Eilenberg, Homological algebra, Princeton, 1956.

    Google Scholar 

  10. A. Dold, Chern classes in general cohomology, Symposia math. vol. v (Geometria), Instituto Naz. di Alta Matematica, Roma (1971).

    MATH  Google Scholar 

  11. -, and R. Lashof, Principal quasifibrations and fibre homotopy equivalence of bundles, Ill. J. Math. 3 (1959), 285–305.

    MathSciNet  MATH  Google Scholar 

  12. E. Dyer, Cohomology theories, Benjamin, 1969.

    Google Scholar 

  13. L. Hodgkin, An equivariant Künneth formula for K-theory, University of Warwick preprint 1968. Ex-homotopy theory, Illinois J. Math. 15 (1971), 324–337.

    MathSciNet  Google Scholar 

  14. S. MacLane, Categorical algebra, Bull. Amer. Math. Soc. 71 (1965), 40–106.

    Article  MathSciNet  MATH  Google Scholar 

  15. S. MacLane, Homology, Springer, 1963.

    Google Scholar 

  16. J. Milnor, Construction of universal bundles II, Ann. of Math. 63 (1956), 430–6.

    Article  MathSciNet  MATH  Google Scholar 

  17. -, On spaces having the homotopy type of a CW-complex, Trans. Amer. Math. Soc. 90 (1959), 272–280.

    MathSciNet  MATH  Google Scholar 

  18. R.S. Palais, The classification of G-spaces, Mem. Amer. Math. Soc. 36 (1960).

    Google Scholar 

  19. M. Rothenberg and N.E. Steenrod, The cohomology of classifying spaces of H-spaces, Bull. Amer. Math. Soc. 71 (1965), 872–5.

    Article  MathSciNet  MATH  Google Scholar 

  20. G. Segal, Equivariant K-theory, Publ. Math. I H E S 34 (1968), 129–151.

    Article  MathSciNet  MATH  Google Scholar 

  21. L. Smith, Lectures on the Eilenberg-Moore spectral sequence, Lecture Notes in Mathematics No. 134, Springer, 1970.

    Google Scholar 

  22. N.E. Steenrod, A convenient category of topological spaces, Mich. Math. J. 14 (1967), 133–152.

    Article  MathSciNet  MATH  Google Scholar 

  23. T. tom Dieck, Faserbündel mit Gruppenoperation, Arch. Math 20 (1969), 136–143.

    Article  MathSciNet  MATH  Google Scholar 

  24. -, Bordism of G-manifolds and integrality theorems. Topology 9 (1970), 345–358.

    Article  MathSciNet  MATH  Google Scholar 

  25. T. tom Dieck, K.H. Kamps, D. Puppe, Homotopietheorie. Lecture Notes in Mathematics no. 157, Springer 1970.

    Google Scholar 

Part II Bibliography

  1. M.F. Atiyah, Characters and cohomology of finite groups, Publ. Math. IHES 9 (1961), 23–64.

    Article  MathSciNet  MATH  Google Scholar 

  2. -, Vector bundles and the Künneth formula, Topology 1 (1962), 245–8.

    Article  MathSciNet  MATH  Google Scholar 

  3. -, K-theory, Benjamin, New York, 1967.

    MATH  Google Scholar 

  4. -, Bott periodicity and the index of elliptic operators, Quarterly J. Math. 19 (1968), 113–140.

    Article  MathSciNet  MATH  Google Scholar 

  5. -, and F. Hirzebruch, Vector bundles and homogeneous spaces, Proc. Sympos. Pure Math. AMS 3 (1961), 7–38.

    Article  MathSciNet  MATH  Google Scholar 

  6. -, and G. Segal, Equivariant K-theory and completion, J. Diff. Geom. 3 (1969), 1–19.

    MathSciNet  MATH  Google Scholar 

  7. A. Borel, Sur la cohomologie des espaces fibrés principaux et des espaces homogenes de groupes de Lie compacts, Ann. Math. 57 (1953), 115–207.

    Article  MathSciNet  MATH  Google Scholar 

  8. -, and F. Hirzebruch, Characteristic classes and homogeneous spaces, Amer. J. Math. 80 (1958), 458–538.

    Article  MathSciNet  MATH  Google Scholar 

  9. N. Bourbaki, Algebre commutative (Éléments de mathématique, fasc. 28), Hermann, Paris, 1961.

    MATH  Google Scholar 

  10. -, Groupes et algebres de Lie (Éléments de mathématique, fasc. 34), Hermann, Paris, 1968.

    MATH  Google Scholar 

  11. E. Cartan, La géométrie des groupes simples, Annali di Mat. 4 (1927), 209–256.

    Article  MathSciNet  MATH  Google Scholar 

  12. H. Cartan and S. Eilenberg, Homological algebra, Princeton, 1956.

    Google Scholar 

  13. A. Dold, Chern classes in general cohomology, Symposia math. 5 (INDAM, Rome, 1970), 385–410.

    Google Scholar 

  14. L.H. Hodgkin, The K-theory of Lie groups, Topology 6 (1967) 1–36.

    Article  MathSciNet  MATH  Google Scholar 

  15. D. Husemoller, Fibre bundles, McGraw-Hill, New York, 1966.

    Book  MATH  Google Scholar 

  16. S. MacLane, Homology, Springer-Verlag, Berlin, 1963.

    Book  MATH  Google Scholar 

  17. H. Pittie, Homogeneous vector bundles on homogeneous spaces, Topology 11 (1972), 199–204.

    Article  MathSciNet  MATH  Google Scholar 

  18. A. Roux, Application de la suite spectrale d'Hodgkin au calcul de la K-théorie des variétés de Stiefel, Bull. Soc. Math. France 99 (1971), 345–368.

    MathSciNet  MATH  Google Scholar 

  19. G. Segal, The representation ring of a compact Lie group, Publ. Math. IHES 34 (1968), 113–128.

    Article  MathSciNet  MATH  Google Scholar 

  20. -, Equivariant K-theory, Publ. Math. IHES 34 (1968), 129–151.

    Article  MathSciNet  MATH  Google Scholar 

  21. V.P. Snaith, Massey products in K-theory II, Proc. Camb. Phil. Soc. 71 (1969), 259–289.

    MathSciNet  MATH  Google Scholar 

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Hodgkin, L. (1975). The equivariant Künneth theorem in K-theorem. In: Topics in K-Theory. Lecture Notes in Mathematics, vol 496. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082285

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  • DOI: https://doi.org/10.1007/BFb0082285

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