Introduction to Differential Topology
by Uwe Kaiser
Publisher: Boise State University 2006
Number of pages: 110
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. Also many more examples of manifolds like matrix groups and Grassmannians are worked out in detail.
Home page url
Download or read it online for free here:
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.
by Ana Cannas da Silva - Princeton University
An overview of symplectic geometry – the geometry of symplectic manifolds. From a language of classical mechanics, symplectic geometry became a central branch of differential geometry and topology. This survey gives a partial flavor on this field.
by Bjorn Ian Dundas - Johns Hopkins University
This is an elementary text book for the civil engineering students with no prior background in point-set topology. This is a rather terse mathematical text, but provided with an abundant supply of examples and exercises with hints.
by Ana Cannas da Silva
The text covers foundations of symplectic geometry in a modern language. It describes symplectic manifolds and their transformations, and explains connections to topology and other geometries. It also covers hamiltonian fields and hamiltonian actions.