Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-05-23T04:46:00.034Z Has data issue: false hasContentIssue false
  • English
  • Français

On the generalised Todd genus of flag bundles

Published online by Cambridge University Press:  20 January 2009

S. A. Ilori
S. A. Ilori
Affiliation:
University of Ibadan, Nigeria
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let V be a complex algebraic variety. Given integers a1, …, am such that

one defines a (a1, …, am)-flag as a nested system

of subspaces of Sn, the n-dimensional complex projective space. The set of all such flags is called an incomplete flag-manifold in Sn, and is denoted by W(al, …, am). Also let E be a complex n-dimensional vector bundle over V. Then we denote by E(a1, …, am−1, n; V) an associated fibre bundle of E with fibre W(a1 − 1, …, am−1 − 1, n − 1). E(a1, …, am−1 − 1, n; V) is called an incomplete flag bundle of E over V (cf. (2), (3)). In Section 10.3 and Section 14.4 of (1), the generalised Todd genus Ty(W(0, n)) and Ty(W(0, 1, …, n)) of the n-dimensional projective space W(0, n) and the flag manifold W(0, 1, …, n) (or F(n+l)) were calculated. Here we compute Ty(W(a1, …, am)) and also Ty(E(a1, …, am−1, n; V)).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 19 , Issue 1 , March 1974 , pp. 35 - 38
Copyright
Copyright © Edinburgh Mathematical Society 1974

References

REFERENCES

(1) Hirzebruch, F.. Topological Methods in Algebraic Geometry, 3rd edition (Springer, Berlin, 1966).Google Scholar
(2) Ingleton, A. W., Tangent flag bundles and generalized Jacobian varieties, Rend. Accad. dei Lincei (1969), 323–329, 505–510.Google Scholar
(3) Séminaire Chevalley (2) 1958, Anneaux de Chow et applications.Google Scholar
(4) Chern, S. S., Hirzebruch, F. and Serre, J.-P., On the index of a fibered manifold. Proc. Amer. Math. Soc. 8 (1957), 587–596.CrossRefGoogle Scholar
(5) Van Der Waerden, B. L., Modern Algebra Vol. I and II (Ungar, New York, 1949).Google Scholar
(6) Borel, A., Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts, Ann. of Math. (2) 57 (1953), 115–207.CrossRefGoogle Scholar
(7) Ehresmann, C., Sur la topologie de certains espaces homogènes, Ann. of Math. (2) 35 (1934), 396–443.CrossRefGoogle Scholar