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1998 | 76 | 2 | 213-228
Tytuł artykułu

On 4-fields and 4-distributions in 8-dimensional vector bundles over 8-complexes

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let ξ be an oriented 8-dimensional spin vector bundle over an 8-complex. In this paper we give necessary and sufficient conditions for ξ to have 4 linearly independent sections or to be a sum of two 4-dimensional spin vector bundles, in terms of characteristic classes and higher order cohomology operations. On closed connected spin smooth 8-manifolds these operations can be computed.
Rocznik
Tom
76
Numer
2
Strony
213-228
Opis fizyczny
Daty
wydano
1998
otrzymano
1996-07-01
poprawiono
1997-08-01
Twórcy
  • Department of Algebra and Geometry, Masaryk University, Janáčkovo nám. 2a, 662 95 Brno, Czech Republic
  • Institute of Mathematics, Academy of Sciences of the Czech Republic, Žižkova 22, 616 62 Brno, Czech Republic
Bibliografia
  • [AR] J. L. Arraut and D. Randall, Index of tangent fields on compact manifolds, in: Contemp. Math. 12, Amer. Math. Soc., 1982, 31-46.
  • [AD] M. Atiyah and J. Dupont, Vector fields with finite singularities, Acta Math. 128 (1972), 1-40.
  • [BH] A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces I, Amer. J. Math. 80 (1958), 458-538.
  • [BS] A. Borel and J. P. Serre, Groupes de Lie et puissances réduites de Steenrod, ibid. 75 (1953), 409-448.
  • [CV1] M. Čadek and J. Vanžura, On the classification of oriented vector bundles over 9-complexes, Rend. Circ. Math. Palermo (2) Suppl. 37 (1994), 33-40.
  • [CV2] M. Čadek and J. Vanžura, On the existence of 2-fields in 8-dimensional vector bundles over 8-com- plexes, Comment. Math. Univ. Carolin. 36 (1995), 377-394.
  • [CV3] M. Čadek and J. Vanžura, Almost quaternionic structures on eight-manifolds, Osaka J. Math., to appear.
  • [CS] M. C. Crabb and B. Steer, Vector-bundle monomorphisms with finite singularities, Proc. London Math. Soc. (3) 30 (1975), 1-39.
  • [D] J. L. Dupont, K-theory obstructions to the existence of vector fields, Acta Math. 113 (1974), 67-80.
  • [H] F. Hirzebruch, Neue topologische Methoden in der algebraischen Geometrie, Ergeb. Math. Grenzgeb. 9, Springer, Berlin, 1959.
  • [K1] U. Koschorke, Vector Fields and Other Vector Bundle Morphisms-a Singularity Approach, Lecture Notes in Math. 847, Springer, 1981.
  • [K2] U. Koschorke, Nonstable and stable monomorhisms of vector bundles, preprint, 1995.
  • [N1] T. B. Ng, 4-fields on (4k+2)-dimensional manifolds, Pacific J. Math. 129 (1987), 337-347.
  • [N2] T. B. Ng, On the geometric dimension of vector bundles, span of a manifold and immersion of manifolds in manifolds, Exposition. Math. 8 (1990), 193-226.
  • [Q] D. Quillen, The mod 2 cohomology rings of extra-special 2-groups and the spinor groups, Math. Ann. 194 (1971), 197-212.
  • [R1] D. Randall, Tangent frame fields on spin manifolds, Pacific J. Math. 76 (1978), 157-167.
  • [R2] D. Randall, On indices of tangent fields with finite singularities, in: Differential Topology (Siegen, 1987), Lecture Notes in Math. 1350, Springer, 1988, 213-240.
  • [T1] E. Thomas, Seminar on Fiber Spaces, Lecture Notes in Math. 13, Springer, Berlin, 1966.
  • [T2] E. Thomas, Postnikov invariants and higher order cohomology operations, Ann. of Math. 85 (1967), 184-217.
  • [T3] E. Thomas, Fields of tangent k-planes on manifolds, Invent. Math. 3 (1967), 334-347.
  • [T4] E. Thomas, Vector fields on manifolds, Bull. Amer. Math. Soc. 75 (1969), 643-683.
  • [W] L. M. Woodward, The classification of orientable vector bundles over CW complexes of small dimension, Proc. Roy. Soc. Edinburgh Sect. A 92 (1982), 175-179.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv76z2p213bwm
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