Principal Bundles and Spaces with a Free Group Action

1 Principal Bundles and Spaces with a Free Group Action 

The bundles become rigid and have interesting structure theory when the fibers are groups that coherently act on themselves. 

Definition 8.10. Let T be a topological group. A principal T-bundle is a fiber bundle E, B,p) with T-action on E such that 

As we shall see later, already the principal Z2-bundles may contain useful information. 

Definition 8.11. Given two principal E-bundles a and 012, bundle map f = fE,fb) between a and 02 is called a principal T-bundle map if the map fs is E-invariant. 

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