Common subbundles and intersections of divisors

Let $V_{0}$ and $V_{1}$ be complex vector bundles over a space $X$ . We use the theory of divisors on formal groups to give obstructions in generalised cohomology that vanish when $V_{0}$ and $V_{1}$ can be embedded in a bundle $U$ in such a way that $V_{0} \cap V_{1}$ has dimension at least $k$ everywhere. We study various algebraic universal examples related to this question, and show that they arise from the generalised cohomology of corresponding topological universal examples. This extends and reinterprets earlier work on degeneracy classes in ordinary cohomology or intersection theory.

Keywords

vector bundle, divisor, degeneracy, Thom–Porteous, formal group

Mathematical Subject Classification 2000

Primary: 55N20

Secondary: 14L05, 14M15

References

Forward citations

Publication

Received: 3 April 2001

Revised: 5 November 2002

Accepted: 19 November 2002

Published: 25 November 2002

Authors

N P Strickland
Department of Mathematics University of Sheffield Western Bank Sheffield, S10 2TN UK

Volume 2, issue 2 (2002)

N P Strickland