Lecture Notes on Seiberg-Witten Invariants
by John Douglas Moore
Publisher: Springer 2010
Number of pages: 130
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.
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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.
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.
by Ville Turunen - Aalto TKK
In this book you will learn something about functional analytic framework of topology. And you will get an access to more advanced literature on non-commutative geometry, a quite recent topic in mathematics and mathematical physics.
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.