Differential Topology and Morse Theory
by Dirk Schuetz
Publisher: University of Sheffield 2009
Number of pages: 96
These notes describe basic material about smooth manifolds (vector fields, flows, tangent bundle, partitions of unity, Whitney embedding theorem, foliations, etc...), introduction to Morse theory, and various applications.
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by Jie Wu - National University of Singapore
Contents: Tangent Spaces, Vector Fields in Rn and the Inverse Mapping Theorem; Topological and Differentiable Manifolds, Diffeomorphisms, Immersions, Submersions and Submanifolds; Examples of Manifolds; Fibre Bundles and Vector Bundles; etc.
by Hansjoerg Geiges - arXiv
This is an introductory text on the more topological aspects of contact geometry. After discussing some of the fundamental results of contact topology, I move on to a detailed exposition of the original proof of the Lutz-Martinet theorem.
by Uwe Kaiser - Boise State University
This is a preliminary version of introductory lecture notes for Differential Topology. We try to give a deeper account of basic ideas of differential topology than usual in introductory texts. Many examples of manifolds are worked out in detail.
by Michael Muger - Radboud University
Contents: Why Differential Topology? Basics of Differentiable Manifolds; Local structure of smooth maps; Transversality Theory; More General Theory; Differential Forms and de Rham Theory; Tensors and some Riemannian Geometry; Morse Theory; etc.