#### Volume 2, issue 2 (2002)

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Common subbundles and intersections of divisors

### N P Strickland

Algebraic & Geometric Topology 2 (2002) 1061–1118
 arXiv: math.AT/0011123
##### Abstract

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