Characteristic Classes and Cobordism, Part 1

1817 LIBRARIES abelian action algebra an+1 Annals of Math arcwise connected BO(n classifying map closed subgroup coefficient system cohomology commutative diagram composite Consider continuous function Corollary corresponds cross-section CW complex define Definition denote diagram commutative Dold element equivalence relation expo fibre bundle finite number following diagram G-map given group G h₂ hence homeomorphism homology identity In-¹ isomorphism Lemma Lie group local coefficient system locally trivial MICHIGAN Milnor monomorphism Note numerable principal G-bundle open cover open sets partition of unity principal G-bundle principal G-space Proof Proposition PX F quotient map Remark Serre fibration Serre spectral sequence SO(n structure group supp Suppose t₁ Theorem topological space topology transition functions trivialisation U₁ UNIVERSITY vector bundle W₁ w₂ x₁ Z₂