On the existence of 2-fields in 8-dimensional vector bundles over 8-complexes
Čadek, Martin ; Vanžura, Jiří
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995), p. 377-394 / Harvested from Czech Digital Mathematics Library

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.

Publié le : 1995-01-01
Classification:  55R25,  57R22,  57R25
@article{118764,
     author = {Martin \v Cadek and Ji\v r\'\i\ Van\v zura},
     title = {On the existence of 2-fields in 8-dimensional vector bundles over 8-complexes},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {36},
     year = {1995},
     pages = {377-394},
     zbl = {0921.57016},
     mrnumber = {1357537},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118764}
}
Čadek, Martin; Vanžura, Jiří. On the existence of 2-fields in 8-dimensional vector bundles over 8-complexes. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) pp. 377-394. http://gdmltest.u-ga.fr/item/118764/

Atiyah M.; Dupont J. Vector fields with finite singularities, Acta Math. (1972), 128 1-40. (1972) | MR 0451256 | Zbl 0233.57010

Borel A. Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts, Ann. Math. (1953), 57 115-207. (1953) | MR 0051508 | Zbl 0052.40001

Frank D. On the index of a tangent $2$-field, Topology (1972), 11 245-252. (1972) | MR 0298689 | Zbl 0252.57006

Hirzebruch F. Neue topologische Methoden in der algebraischen Geometrie, Ergebnisse der Mathematik und ihrer Grenzgebiete, Heft 9, Berlin (1959). (1959)

Kono A. On the integral cohomology of $BSpin(n)$, J. Math. Kyoto Univ. (1986), 26:3 333-337. (1986) | MR 0857221 | Zbl 0617.55007

Massey W.S. On the Stiefel-Whitney classes of a manifold II, Proc. Amer. Math. Soc. (1962), 13 938-942. (1962) | MR 0142129 | Zbl 0109.15902

Milnor J. Some consequences of a theorem of Bott, Ann. of Math. (1958), 68 444-449. (1958) | MR 0102805 | Zbl 0085.17301

Mosher R.E.; Tangora M.C. Cohomology operations and applications in homotopy theory, Harper & Row, Publishers New York, Evanston and London (1968). (1968) | MR 0226634 | Zbl 0153.53302

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. (1990) | MR 1062767

Paechter G. The groups $\pi_r(V_{n,m})$: I, Quart. J. Math., Oxford Ser. (2) (1956), 7 243-268. (1956) | MR 0131878

Quillen D. The mod $2$ cohomology rings of extra-special $2$-groups and the spinor groups, Math. Ann. (1971), 194 197-212. (1971) | MR 0290401 | Zbl 0225.55015

Thomas E. The index of a tangent $2$-field, Comment. Math. Helvet. (1967), 42 86-110. (1967) | MR 0215317 | Zbl 0153.53504

Thomas E. Complex structures on real vector bundles, Am. J. Math. (1966), 89 887-908. (1966) | MR 0220310

Thomas E. On the cohomology of the real Grassmann complexes, Trans. Amer. Math. Soc. (1960), 96 67-89. (1960) | MR 0121800 | Zbl 0098.36301

Thomas E. On the cohomology groups of the classifying space for the stable spinor group, Bol. Soc. Math. Mex. (1962), 57-69. (1962) | MR 0153027 | Zbl 0124.16401

Thomas E. Postnikov invariants and higher order cohomology operation, Ann. of Math. (1967), 85 184-217. (1967) | MR 0210135