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Vector Fields and Other Vector Bundle Morphisms - A Singularity Approach
Limited preview - 2006
apply assume Atiyah and Dupont bijective bordant bordism class boundary canonical line bundle characteristic number classifying map closed connected n-manifold closed n-manifold closed smooth Coker commuting diagram compact corresponding defined denote equation exact sequence example extend fact finite singularities forgetful map hence homomorphism homotopy classes homotopy group identify implies injective integer invariant isomorphism k-field with finite k-framefield k-morphism ker f kernel lemma manifold of dimension Math monomorphism Moreover morphism nondegenerate nonorientable nontrivial normal bordism groups normal bundle obstruction obtain obvious orientable manifold orientation bundle paracompact space proof of theorem proposition pullback resp result singularity data smooth manifold span span(Sn sphere bundle stable span(M Stiefel-Whitney class suitable tangent tangent bundle tangent map theorem 9.3 theory Topology trivial uk(M unoriented vanishes vector bundle vectorfield zero bordism zero set