Fibre bundles first arose as bundles associated with the geometry of a manifold. In this chapter we consider topics in the topology of manifolds connected with vector bundles and the orientability of manifolds. Using Stiefel-Whitney classes we derive elementary nonexistence theorems for immersions of manifolds into euclidean space.
KeywordsExact Sequence Vector Bundle Tangent Bundle Normal Bundle Closed Manifold
Unable to display preview. Download preview PDF.