 # Differential Topology

## e-books in Differential Topology category Contact Topology
by - 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.
(3647 views) Differential Topology
by - 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.
(10180 views) Differential Topology and Morse Theory
by - University of Sheffield ,
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.
(10213 views) Differential Topology of Fiber Bundles
by - 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.
(9328 views) Introduction to Differential Topology, de Rham Theory and Morse Theory
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.
(11327 views) Introduction to Differential Topology
by - 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.
(9344 views) Contact Geometry
by - 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.
(10870 views) Ricci Flow and the Poincare Conjecture
by - American Mathematical Society ,
This book provides full details of a complete proof of the Poincare Conjecture following Grigory Perelman's preprints. The book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology.
(12224 views) Lecture Notes on Differentiable Manifolds
by - 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.
(11458 views) Tight and Taut Submanifolds
by - Cambridge University Press ,
Tight and taut submanifolds form an important class of manifolds with special curvature properties, one that has been studied intensively by differential geometers since the 1950's. This book contains six articles by leading experts in the field.
(10907 views) Introduction to Symplectic and Hamiltonian Geometry
by ,
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.
(13752 views) Manifolds of Differentiable Mappings
by - 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.
(9872 views) Lectures on Symplectic Geometry
by - Springer ,
An introduction to symplectic geometry and topology, it provides a useful and effective synopsis of the basics of symplectic geometry and serves as the springboard for a prospective researcher. The text is written in a clear, easy-to-follow style.
(14294 views) Symplectic Geometry
by - 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.
(11964 views) Differentiable Manifolds
by ,
The historical driving force of the theory of manifolds was General Relativity, where the manifold is four-dimensional spacetime, wormholes and all. This text is occupied with the theory of differential forms and the exterior derivative.
(18076 views)