## see also

## e-books in Differential Topology category

**Differential Topology**

by

**Bjorn Ian Dundas**-

**Johns Hopkins University**,

**2002**

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.

(

**5500**views)

**Differential Topology and Morse Theory**

by

**Dirk Schuetz**-

**University of Sheffield**,

**2009**

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.

(

**5523**views)

**Differential Topology of Fiber Bundles**

by

**Karl-Hermann Neeb**-

**FAU Erlangen-Nuernberg**,

**2010**

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.

(

**4972**views)

**Introduction to Differential Topology, de Rham Theory and Morse Theory**

by

**Michael Muger**-

**Radboud University**,

**2005**

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.

(

**6183**views)

**Introduction to Differential Topology**

by

**Uwe Kaiser**-

**Boise State University**,

**2006**

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.

(

**5430**views)

**Contact Geometry**

by

**Hansjoerg Geiges**-

**arXiv**,

**2004**

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.

(

**6151**views)

**Ricci Flow and the Poincare Conjecture**

by

**John Morgan, Gang Tian**-

**American Mathematical Society**,

**2007**

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.

(

**6800**views)

**Lecture Notes on Differentiable Manifolds**

by

**Jie Wu**-

**National University of Singapore**,

**2004**

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.

(

**7127**views)

**Tight and Taut Submanifolds**

by

**Thomas E. Cecil, Shiing-shen Chern**-

**Cambridge University Press**,

**1997**

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.

(

**6099**views)

**Introduction to Symplectic and Hamiltonian Geometry**

by

**Ana Cannas da Silva**,

**2007**

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.

(

**8856**views)

**Manifolds of Differentiable Mappings**

by

**Peter W. Michor**-

**Birkhauser**,

**1980**

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.

(

**5395**views)

**Lectures on Symplectic Geometry**

by

**Ana Cannas da Silva**-

**Springer**,

**2006**

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.

(

**9014**views)

**Symplectic Geometry**

by

**Ana Cannas da Silva**-

**Princeton University**,

**2004**

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.

(

**7759**views)

**Differentiable Manifolds**

by

**Nigel Hitchin**,

**2003**

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.

(

**11972**views)