The Lyusternik-Shnirel'man category, vector bundles, and immersions of manifolds (Q1384671)

The author's summary: ``One of our two main results exhibits for a vector bundle over a compact Hausdorff space \(X\) an interplay between its span, its possible splittings, and the Lyusternik-Shnirel'man category of \(X\). The other main result, also on vector bundles and the Lyusternik-Shnirel'man category, enables us to derive certain inequalities connecting the immersion codimension, the stable span, and the Lyusternik-Shnirel'man category of a smooth closed manifold which is not stably parallelizable. Our results are applicable in various situations of general interest''.