Common subbundles and intersections of divisors

Details Common subbundles and intersections of divisors Common subbundles and intersections of divisors

2000-11-17

arxiv.org/abs/math/0011123v3

Algebr. Geom. Topol. 2 (2002) 1061-1118

Mathematics

Algebraic Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-42.abs.html

Scientific paper

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.

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