Mathematics Colloquia and Seminars

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Characteristic classes encode important topological data of vector bundles over manifolds. Stiefel-Whitney classes are a primary example of characteristic classes on real vector bundles. First, I will review the basics of vector bundles, then explain how compute the Stiefel-Whitney classes on typical bundles, and finaly show how to use Stiefel-Whitney classes to determine whether a manifold can admit nowhere zero vector fields and as well as how to determine conditions ambient spaces necessary to immerse real projective manifolds.