**Lecture Notes on Seiberg-Witten Invariants**

by John Douglas Moore

**Publisher**: Springer 2010**ISBN/ASIN**: 3540412212**ISBN-13**: 9783540412212**Number of pages**: 130

**Description**:

This book gives a streamlined introduction to the theory of Seiberg-Witten invariants suitable for second-year graduate students. These invariants can be used to prove that there are many compact topological four-manifolds which have more than one smooth structure, and that others have no smooth structure at all. This topic provides an excellent example of how global analysis techniques, which have been developed to study nonlinear partial differential equations, can be applied to the solution of interesting geometrical problems.

Download or read it online for free here:

**Download link**

(550KB, PDF)

## Similar books

**Manifolds and Differential Forms**

by

**Reyer Sjamaar**-

**Cornell University**

The text covers manifolds and differential forms for an audience of undergraduates who have taken a typical calculus sequence, including basic linear algebra and multivariable calculus up to the integral theorems of Green, Gauss and Stokes.

(

**12952**views)

**Manifolds**

by

**Neil Lambert**-

**King's College London**

From the table of contents: Manifolds (Elementary Topology and Definitions); The Tangent Space; Maps Between Manifolds; Vector Fields; Tensors; Differential Forms; Connections, Curvature and Metrics; Riemannian Manifolds.

(

**9945**views)

**Optimization Algorithms on Matrix Manifolds**

by

**P.-A. Absil, R. Mahony, R. Sepulchre**-

**Princeton University Press**

Many science and engineering problems can be rephrased as optimization problems on matrix search spaces endowed with a manifold structure. This book shows how to exploit the structure of such problems to develop efficient numerical algorithms.

(

**17931**views)

**Noncommutative Localization in Algebra and Topology**

by

**Andrew Ranicki**-

**Cambridge University Press**

Noncommutative localization is a technique for constructing new rings by inverting elements, matrices and more generally morphisms of modules. The applications to topology are via the noncommutative localizations of the fundamental group rings.

(

**9370**views)