**Differentiable Manifolds**

by Nigel Hitchin

2003**Number of pages**: 94

**Description**:

This is an introductory course on differentiable manifolds. One of the historical driving forces of the theory of manifolds was General Relativity, where the manifold is four-dimensional spacetime, wormholes and all. A large part of the text is occupied with the theory of differential forms and the exterior derivative.

Download or read it online for free here:

**Download link**

(1MB, PDF)

## Similar books

**Differential Topology and Morse Theory**

by

**Dirk Schuetz**-

**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.

(

**11696**views)

**Ricci Flow and the Poincare Conjecture**

by

**John Morgan, Gang Tian**-

**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.

(

**13995**views)

**Introduction to Symplectic and Hamiltonian Geometry**

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.

(

**15141**views)

**Differential Topology of Fiber Bundles**

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.

(

**10603**views)