Good Resource on Universal Bundles?

Question

I am looking to learn about universal bundles and classifying spaces as I came across a question which a professor I'm working with suggested is related to these objects, but they don't appear in any textbook I have. Appreciate any suggestions.

Answer 1

I think Vector Bundles and K-theory by Allen Hatcher provides a good resource for the study of universal bundles. For classifying spaces there is this brief post http://math.ucr.edu/home/baez/calgary/BG.html of John Baez that contains some references.

Have in mind that these topics require some familiarity with vector bundles, principal bundles and homotopy groups.

Answer 2

I would recommend 'Fibre Bundles' by Dale Husemoller