This book offers an introduction to the theory of differentiable
manifolds and fiber bundles. It examines bundles from the point of
view of metric differential geometry: Euclidean bundles, Riemannian
connections, curvature, and Chern-Weil theory are discussed,
including the Pontrjagin, Euler, and Chern characteristic classes
of a vector bundle. These concepts are illustrated in detail for
bundles over spheres.
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