#### Algebraic and Geometric Topology 2 (2002),
paper no. 42, pages 1061-1118.

## Common subbundles and intersections of divisors

### N. P. Strickland

**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

**AMS subject classification**.
Primary: 55N20.
Secondary: 14L05,14M15.

**DOI:** 10.2140/agt.2002.2.1061

**E-print:** `arXiv:math.AT/0011123`

Submitted: 3 April 2001.
(Revised: 5 November 2002.)
Accepted: 19 November 2002.
Published: 25 November 2002.

Notes on file formats
N. P. Strickland

Department of Mathematics, University of Sheffield

Western Bank, Sheffield, S10 2TN,UK

Email: N.P.Strickland@sheffield.ac.uk

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