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Please enable cookies in your browser to get the full Trove experience. Skip to content Skip to search. Moore, John D. Language English View all editions Prev Next edition 4 of 9.

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Author Moore, John D. Series Lecture notes in mathematics, ; Lecture notes in mathematics Springer-Verlag ; Part Of Springer e-books. Subjects Statistical physics. Mathematical optimization.

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Systems theory. Global differential geometry. Systems Theory, Control. Global analysis Mathematics Global analysis. Four-manifolds Topology Summary In the fall of , Edward Witten proposed a set of equations which give the main results of Donaldson theory in a far simpler way than had been thought possible. The purpose of these notes is to provide an elementary introduction to the equations that Witten proposed.

They are directed towards graduate students who have already taken a basic course in differential geometry and topology. Contents 1. What is a vector bundle? What is a connection? The curvature of a connection.

Characteristic classes. The universal bundle. Classification of connections. Hodge theory 2. Spin geometry on four-manifolds. Euclidean geometry and the spin groups.

What is a spin structure? Almost complex and spin[superscript]c structures. Clifford algebras.

Lecture Notes on Seiberg-Witten Invariants - Download link

The spin connection. The Dirac operator. The Atiyah-Singer Index Theorem 3.

Seiberg-Witten Theory, Part 2 - Edward Witten

Global analysis of the Seiberg-Witten equations. The Seiberg-Witten equations. The moduli space.

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Compactness of the moduli space. Topology of four-manifolds. Seiberg-Witten invariants. Dirac operators on Kahler surfaces. Invariants of Kahler surfaces.

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