Fibre Bundles (Graduate Texts in Mathematics 20)
by Dale Husemöller · Springer
Where Steenrod is the classical source, Husemöller is the modern working reference: the book that treats associated bundles and gauge groups at length, which the topic note calls out directly. Graduate Texts in Mathematics volume covering bundle basics, homotopy classification, principal and associated bundles, K-theory, and, added in the third edition, the gauge group of a bundle and differential forms representing characteristic classes of complex vector bundles.
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