Principal Bundles

Abstract

A principal bundle is a fiber bundle with a group as typical fiber. Fiber bundles are spaces which locally look like product spaces. In this text, we will classify all numerable principal bundles. That are principal bundles with a suitable partition of unity on the orbit space. In order to do this many tools for principal bundles and partitions of unities are created. We construct universal bundles, using both the Milnor construction and configuration spaces. The latter are used to link principal bundles for symmetric groups with finitely sheeted covering spaces. Lastly, lifting properties on principal bundles are considered.