In the fall of 1994, 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
CONTENT
Preliminaries -- Spin geometry on four-manifolds -- Global analysis of the Seiberg-Witten equations
SUBJECT
Mathematics
Algebra
Global analysis (Mathematics)
Manifolds (Mathematics)
System theory
Differential geometry
Calculus of variations
Statistical physics
Dynamical systems
Mathematics
Global Analysis and Analysis on Manifolds
Systems Theory
Control
Calculus of Variations and Optimal Control; Optimization