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Parallelizability of homogeneous spaces, II

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References

  1. Araki, S.: Differential Hopf algebras and the cohomology mod 3 of the compact exceptional groupsE 7 andE 8. Ann. Math.73, 404–436 (1961)

    Google Scholar 

  2. Araki, S.: Cohomology modulo 2 of the compact exceptional groupsE 6 andE 7. J. Math. Osaka Univ., Ser. A,12, 43–65 (1961)

    Google Scholar 

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

    Google Scholar 

  4. Atiyah, M.F., Hitchin, N.J., Singer, I.M.: Self-duality in four-dimensional Riemannian geometry. Proc. R. Soc. Lond. Ser. A,362, 425–461 (1978)

    Google Scholar 

  5. Becker, J.C.: The real semi-characteristic of a homogeneous space. Ill. J. Math.25, 577–588 (1981)

    Google Scholar 

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

    Google Scholar 

  7. Borel, A.: Sur l'homologie et la cohomologie des groupes de Lie compacts connexes. Am. J. Math.76, 272–342 (1954)

    Google Scholar 

  8. Borel, A.: Sous-groupes commutatifs et torsion des groupesde Lie compacts connexes. Tohoku Math. J., Ser. II,13, 216–240 (1961)

    Google Scholar 

  9. Borel, A., Hirzebruch, F.: Characteristic classes and homogeneous spaces, I. Am. J. Math.80, 458–538 (1958)

    Google Scholar 

  10. Bott, R., Samelson, H.: Application of the theory of Morse to symmetric spaces. Am. J. Math.80, 964–1029 (1958)

    Google Scholar 

  11. Bourbaki, N.: Groupes et algèbres de Lie, Chap. IV–VIII. Paris: Hermann 1968, 1975

    Google Scholar 

  12. Bröcker, Th., Dieck, T. tom: Representations of compact Lie groups. Berlin, Heidelberg, New York, Tokyo: Springer 1985

    Google Scholar 

  13. Dynkin, E.B.: Semisimple subalgebras of semisimple Lie algebras. Am. Math. Soc. Transl., Ser. 2,6, 111–244 (1957)

    Google Scholar 

  14. Dynkin, E.B.: Topological characteristics of homomorphisms of compact Lie groups. Am. Math. Soc. Transl., Ser. 2,12, 301–342 (1959)

    Google Scholar 

  15. Feshbach, M.: The image ofH *(BG;ℤ) inH *(BT;ℤ) forG a compact Lie group with maximal torusT. Topology20, 93–95 (1981)

    Google Scholar 

  16. Gugenheim, V.K.A.M., May, J.P.: On the theory and applications of differential torsion products. Mem. Am. Math. Soc.142 (1974)

  17. Hsiang, W.-Y.: On characteristic classes of compact homogeneous spaces and their applications in compact transformation groups. Bol. Soc. Bras. Mat.10, 87–162 (1979)

    Google Scholar 

  18. Kono, A., Mimura, M.: Cohomology mod 2 of the classifying space of the compact Lie group of typeE 6. J. Pure Appl. Alg.6, 61–81 (1975)

    Google Scholar 

  19. Kono, A., Mimura, M., Shimada, N.: On the cohomology mod 2 of the classifying space of the 1-connected exceptional Lie groupE 7. J. Pure Appl. Alg.8, 267–283 (1976)

    Google Scholar 

  20. Löffler, P., Smith, L.: Line bundles over framed manifolds. Math. Z.138, 35–52 (1974)

    Google Scholar 

  21. McKay, W.G., Patera, J.: Tables of dimensions, indices, and branching rules for representations of simple Lie algebras. New York, Basel: Dekker 1981

    Google Scholar 

  22. Miatello, I.D., Miatello, R.J.: On stable parallelizability ofτ~ k, n and related manifolds. Math. Ann.259, 343–350 (1982)

    Google Scholar 

  23. Oniščik, A.L.: Torsion of special Lie groups. Am. Math. Soc. Transl., Ser. 2,50, 1–4 (1966)

    Google Scholar 

  24. Quillen, D.: The mod 2 cohomology rings of extra-special 2-groups and spinor groups. Math. Ann.194, 197–212 (1971)

    Google Scholar 

  25. Singhof, W.: Parallelizability of homogeneous spaces, I. Math. Ann.260, 101–116 (1982)

    Google Scholar 

  26. Snaith, V.P.: Massey products inK-theory II. Proc. Camb. Phil. Soc.69, 259–289 (1971)

    Google Scholar 

  27. Stong, R.E.: Semicharacteristics and free group actions. Compos. Math.29, 223–248 (1974)

    Google Scholar 

  28. Stong, R.E.: Semicharacteristics of oriented Grasmannians (to appear)

  29. Wang, M.Y.K.: Some remarks on the calculation of Stiefel-Whitney classes and a paper of Wu-Yi Hsiang's. Pac. J. Math.112, 431–444 (1984)

    Google Scholar 

  30. Warner, G.: Harmonic analysis on semi-simple Lie groups II. Berlin, Heidelberg, New York: Springer 1972

    Google Scholar 

  31. Watanabe, T.: The integral cohomology ring of the symmetric space E VII. J. Math. Kyoto Univ.15, 363–385 (1975)

    Google Scholar 

  32. Wemmer, D.: Stabil parallelisierbare homogene Räume. Thesis, Köln 1985

  33. Whitehead, G.W.: Elements of Homotopy Theory. Berlin, Heidelberg, New York: Springer 1978

    Google Scholar 

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  1. Mathematisches Institut, Universität Köln, Weyertal 86-90, D-5000, Köln 41, Germany

    Wilhelm Singhof & Dieter Wemmer

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  1. Wilhelm Singhof
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Singhof, W., Wemmer, D. Parallelizability of homogeneous spaces, II. Math. Ann. 274, 157–176 (1986). https://doi.org/10.1007/BF01458022

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