The author proves several embedding theorems for finite covering maps, principal G-bundlesinto bundles. The main results are1. Let π: E→X be a finite covering mapt and X a connected locally pathconnectedparacompact ...The author proves several embedding theorems for finite covering maps, principal G-bundlesinto bundles. The main results are1. Let π: E→X be a finite covering mapt and X a connected locally pathconnectedparacompact space. If cat X≤5 k, then the finite covering space π: E→X can be embeddedinto the trivial real k-plane bundle.2. Let x: E→ X be a principal G-bundle over a paracompact space. If there exists alinear action of G on F (F = R or C) and cat X≤ k, then π: E→X can be embedded intofor any F-vector bundles ζi, i = 1,’’’ k.展开更多
文摘The author proves several embedding theorems for finite covering maps, principal G-bundlesinto bundles. The main results are1. Let π: E→X be a finite covering mapt and X a connected locally pathconnectedparacompact space. If cat X≤5 k, then the finite covering space π: E→X can be embeddedinto the trivial real k-plane bundle.2. Let x: E→ X be a principal G-bundle over a paracompact space. If there exists alinear action of G on F (F = R or C) and cat X≤ k, then π: E→X can be embedded intofor any F-vector bundles ζi, i = 1,’’’ k.
