Chapter 4

Smooth Manifolds

Abstract

In this chapter we first introduce the notion of a manifold, and then of a smooth structure on a manifold, a manifold together with a smooth structure on it being a smooth manifold. In fact we introduce the more general notion of a (smooth) manifold with boundary. We see how to generalize the basic notions we have introduced for regions in image to general smooth manifolds with boundary: the notions of tangent vectors and differential forms. We see how to do calculations with differential forms on smooth manifolds with boundary: using the notion of a pull-back, we reduce these to computations in . We introduce the ...

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