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.

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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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