Principal Bundles
Summary
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.