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

Martin Čadek; Jiří Vanžura

Colloquium Mathematicae (1996)

  • Volume: 70, Issue: 1, page 25-40
  • ISSN: 0010-1354

Abstract

top
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.

How to cite

top

Čadek, Martin, and Vanžura, Jiří. "On 2-distributions in 8-dimensional vector bundles over 8-complexes." Colloquium Mathematicae 70.1 (1996): 25-40. <http://eudml.org/doc/210394>.

@article{Čadek1996,
abstract = {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.},
author = {Čadek, Martin, Vanžura, Jiří},
journal = {Colloquium Mathematicae},
keywords = {secondary cohomology operation; classifying spaces for groups; vector bundle; characteristic classes; Postnikov tower; distribution},
language = {eng},
number = {1},
pages = {25-40},
title = {On 2-distributions in 8-dimensional vector bundles over 8-complexes},
url = {http://eudml.org/doc/210394},
volume = {70},
year = {1996},
}

TY - JOUR
AU - Čadek, Martin
AU - Vanžura, Jiří
TI - On 2-distributions in 8-dimensional vector bundles over 8-complexes
JO - Colloquium Mathematicae
PY - 1996
VL - 70
IS - 1
SP - 25
EP - 40
AB - 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.
LA - eng
KW - secondary cohomology operation; classifying spaces for groups; vector bundle; characteristic classes; Postnikov tower; distribution
UR - http://eudml.org/doc/210394
ER -

References

top
  1. [AD] M. Atiyah and J. Dupont, Vector fields with finite singularities, Acta Math. 128 (1972), 1-40. Zbl0233.57010
  2. [CS] M. C. Crabb and B. Steer, Vector bundle monomorphisms with finite singularities, Proc. London Math. Soc. (3) 30 (1975), 1-39. Zbl0294.57015
  3. [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. Zbl0921.57016
  4. [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. Zbl0853.57026
  5. [H] F. Hirzebruch, Neue topologische Methoden in der algebraischen Geometrie, Ergeb. Math. Grenzgeb. 9, Springer, Berlin, 1959. Zbl0101.38301
  6. [K] U. Koschorke, Vector Fields and Other Vector Bundle Morphisms - a Singularity Approach, Lecture Notes in Math. 847, Springer, 1981. Zbl0459.57016
  7. [M] M. H. de Paula Leite Mello, Two plane sub-bundles of nonorientable real vector bundles, Manuscripta Math. 57 (1987), 263-280. Zbl0602.55009
  8. [Q] D. Quillen, The mod 2 cohomology rings of extra-special 2-groups and the spinor groups, Math. Ann. 194 (1971), 197-212. Zbl0225.55015
  9. [D] D. Randall, CAT 2-fields on nonorientable CAT manifolds, Quart. J. Math. Oxford (2) 38 (1987), 355-366. Zbl0628.57015
  10. [T1] E. Thomas, Fields of tangent 2-planes on even dimensional manifolds, Ann. of Math. 86 (1967), 349-361. Zbl0168.21401
  11. [T2] E. Thomas, Complex structures on real vector bundles, Amer. J. Math. 89 (1966), 887-908. Zbl0174.54802
  12. [T3] E. Thomas, Postnikov invariants and higher order cohomology operations, Ann. of Math. 85 (1967), 184-217. Zbl0152.22002
  13. [T4] E. Thomas, Fields of tangent k-planes on manifolds, Invent. Math. 3 (1967), 334-347. Zbl0162.55402

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.