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span of the vector bundle; classifying spaces for spinor groups; characteristic classes; Postnikov tower; secondary cohomology operation
Necessary and sufficient conditions for the existence of two linearly independent sections in an 8-dimensional spin vector bundle over a CW-complex of the same dimension are given in terms of characteristic classes and a certain secondary cohomology operation. In some cases this operation is computed.
[AD] Atiyah M., Dupont J.: Vector fields with finite singularities. Acta Math. (1972), 128 1-40. MR 0451256 | Zbl 0233.57010
[B] Borel A.: Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts. Ann. Math. (1953), 57 115-207. MR 0051508 | Zbl 0052.40001
[F] Frank D.: On the index of a tangent $2$-field. Topology (1972), 11 245-252. MR 0298689 | Zbl 0252.57006
[H] Hirzebruch F.: Neue topologische Methoden in der algebraischen Geometrie. Ergebnisse der Mathematik und ihrer Grenzgebiete, Heft 9, Berlin (1959).
[K] Kono A.: On the integral cohomology of $BSpin(n)$. J. Math. Kyoto Univ. (1986), 26:3 333-337. MR 0857221 | Zbl 0617.55007
[Ma] Massey W.S.: On the Stiefel-Whitney classes of a manifold II. Proc. Amer. Math. Soc. (1962), 13 938-942. MR 0142129 | Zbl 0109.15902
[M] Milnor J.: Some consequences of a theorem of Bott. Ann. of Math. (1958), 68 444-449. MR 0102805 | Zbl 0085.17301
[MT] Mosher R.E., Tangora M.C.: Cohomology operations and applications in homotopy theory. Harper & Row, Publishers New York, Evanston and London (1968). MR 0226634 | Zbl 0153.53302
[Ng] Tze-Beng Ng: On the geometric dimension of the vector bundles, span of a manifold and immersions of manifolds in manifolds. Exposition. Math. (1990), 8 193-226. MR 1062767
[P] Paechter G.: The groups $\pi_r(V_{n,m})$: I. Quart. J. Math., Oxford Ser. (2) (1956), 7 243-268. MR 0131878
[Q] Quillen D.: The mod $2$ cohomology rings of extra-special $2$-groups and the spinor groups. Math. Ann. (1971), 194 197-212. MR 0290401 | Zbl 0225.55015
[T1] Thomas E.: The index of a tangent $2$-field. Comment. Math. Helvet. (1967), 42 86-110. MR 0215317 | Zbl 0153.53504
[T2] Thomas E.: Complex structures on real vector bundles. Am. J. Math. (1966), 89 887-908. MR 0220310
[T3] Thomas E.: On the cohomology of the real Grassmann complexes. Trans. Amer. Math. Soc. (1960), 96 67-89. MR 0121800 | Zbl 0098.36301
[T4] Thomas E.: On the cohomology groups of the classifying space for the stable spinor group. Bol. Soc. Math. Mex. (1962), 57-69. MR 0153027 | Zbl 0124.16401
[T5] Thomas E.: Postnikov invariants and higher order cohomology operation. Ann. of Math. (1967), 85 184-217. MR 0210135
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