 
Summary: Lecture Notes on SeibergWitten Invariants
(Revised Second Edition)
John Douglas Moore
July, 2010
Preface
Riemannian, symplectic and complex geometry are often studied by means
of solutions to systems of nonlinear differential equations, such as the equa
tions of geodesics, minimal surfaces, pseudoholomorphic curves and Yang
Mills connections. For studying such equations, a new unified technology
has been developed, involving analysis on infinitedimensional manifolds.
A striking applications of the new technology is Donaldson's theory of
"antiselfdual" connections on SU(2)bundles over fourmanifolds, which
applies the YangMills equations from mathematical physics to shed light
on the relationship between the classification of topological and smooth
fourmanifolds. This reverses the expected direction of application from
topology to differential equations to mathematical physics. Even though
the YangMills equations are only mildly nonlinear, a prodigious amount
of nonlinear analysis is necessary to fully understand the properties of the
space of solutions.
At the present state of knowledge, understanding smooth structures on
