Common subbundles and intersections of divisors
Neil P. Strickland
55N20 14L05 14M15
Department of Pure Mathematics
University of Sheffield
Hicks Building
Hounsfield Road
Sheffield S3 7RH
UK
N.P.Strickland@sheffield.ac.uk
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 the intersection of V_0 and 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.