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 George Torres, Robert Gompf - University of Texas at Austin
This is a course on contact manifolds, which are odd dimensional manifolds with an extra structure called a contact structure. Most of our study will focus on three dimensional manifolds, though many of these notions hold for any odd dimension.
by Peter W. Michor - Birkhauser
This book is devoted to the theory of manifolds of differentiable mappings and contains result which can be proved without the help of a hard implicit function theorem of nuclear function spaces. All the necessary background is developed in detail.
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 Karl-Hermann Neeb - FAU Erlangen-Nuernberg
From the table of contents: Basic Concepts (The concept of a fiber bundle, Coverings, Morphisms...); Bundles and Cocycles; Cohomology of Lie Algebras; Smooth G-valued Functions; Connections on Principal Bundles; Curvature; Perspectives.