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1996 | 70 | 1 | 25-40
Tytuł artykułu

On 2-distributions in 8-dimensional vector bundles over 8-complexes

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
It is shown that the $ℤ_2$-index of a 2-distribution in an 8-dimensional spin vector bundle over an 8-complex is independent of the 2-distribution. Necessary and sufficient conditions for the existence of 2-distributions in such vector bundles are given in terms of characteristic classes and a certain secondary cohomology operation. In some cases this operation is computed.
Rocznik
Tom
70
Numer
1
Strony
25-40
Opis fizyczny
Daty
wydano
1996
otrzymano
1994-10-10
poprawiono
1995-03-24
Twórcy
  • Institute of Mathematics, Academy of Sciences of the Czech Republic, Žižkova 22, 616 62 Brno, Czech Republic
  • Institute of Mathematics, Academy of Sciences of the Czech Republic, Žižkova 22, 616 62 Brno, Czech Republic
Bibliografia
  • [AD] M. Atiyah and J. Dupont, Vector fields with finite singularities, Acta Math. 128 (1972), 1-40.
  • [CS] M. C. Crabb and B. Steer, Vector bundle monomorphisms with finite singularities, Proc. London Math. Soc. (3) 30 (1975), 1-39.
  • [CV1] M. Čadek and J. Vanžura, On the existence of 2-fields in 8-dimensional vector bundles over 8-complexes, Comment. Math. Univ. Carolin. (1995), to appear.
  • [CV2] M. Čadek and J. Vanžura, On the classification of oriented vector bundles over 9-complexes, Proceedings of the Winter School Geometry and Physics 1993, Suppl. Rend. Circ. Math. Palermo (2) 37 (1994), 33-40.
  • [H] F. Hirzebruch, Neue topologische Methoden in der algebraischen Geometrie, Ergeb. Math. Grenzgeb. 9, Springer, Berlin, 1959.
  • [K] U. Koschorke, Vector Fields and Other Vector Bundle Morphisms - a Singularity Approach, Lecture Notes in Math. 847, Springer, 1981.
  • [M] M. H. de Paula Leite Mello, Two plane sub-bundles of nonorientable real vector bundles, Manuscripta Math. 57 (1987), 263-280.
  • [Q] D. Quillen, The mod 2 cohomology rings of extra-special 2-groups and the spinor groups, Math. Ann. 194 (1971), 197-212.
  • [D] D. Randall, CAT 2-fields on nonorientable CAT manifolds, Quart. J. Math. Oxford (2) 38 (1987), 355-366.
  • [T1] E. Thomas, Fields of tangent 2-planes on even dimensional manifolds, Ann. of Math. 86 (1967), 349-361.
  • [T2] E. Thomas, Complex structures on real vector bundles, Amer. J. Math. 89 (1966), 887-908.
  • [T3] E. Thomas, Postnikov invariants and higher order cohomology operations, Ann. of Math. 85 (1967), 184-217.
  • [T4] E. Thomas, Fields of tangent k-planes on manifolds, Invent. Math. 3 (1967), 334-347.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-cmv70i1p25bwm
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