**Differentiable Manifolds**

by Nigel Hitchin

2003

**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**

(ZIP/PDF)

## Similar books

**Differential Topology**

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.

(

**6636**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.

(

**7942**views)

**Symplectic Geometry**

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.

(

**8689**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.

(

**5955**views)