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
Topology and Physics: A Historical Essayby C. Nash - arXiv
In this essay we wish to embark on the telling of a story which, almost certainly, stands only at its beginning. We shall discuss the links and the interaction between one very old subject, physics, and a much newer one, topology.
(14948 views)
Manifoldsby 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.
(10639 views)
Lectures on Sheaf Theoryby C.H. Dowker - Tata Institute of Fundamental Research
A sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space. Contents: Sheaves; Sections; Cohomology groups of a space with coefficients in a presheaf; Introduction of the family Phi; etc.
(11030 views)
Optimization Algorithms on Matrix Manifoldsby 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.
(18809 views)