Seiberg-Witten invariants
(a minicourse, 8 lectures)

Seiberg-Witten invariants are one of the most powerful tools in
4-dimensional topology and symplectic geometry. I would give a
self-contained introduction to basic properties of Seiberg-Witten
invariants of 4-dimensional manifolds. I will introduce the Clifford
algebras, explain the Bott periodicity for Clifford algebras, define
the $Spin$ and $Spin^c$-structures, the Seiberg-Witten equation, the
Weitzenbock formula, explain the compactness of the space of solutions
of the Seiberg-Witten equation, and compute the Seiberg-Witten
invariants of Kahler surfaces.

Site of the mini-course: http://verbit.ru/IMPA/SW-2026

Literature:

Lawson, H. B., Michelsohn, M.-L., Spin Geometry (1989)

John W. Morgan, The Seiberg-Witten Equations and Applications
to the Topology of Smooth Four-Manifolds (1995)

Liviu I. Nicolaescu, Notes on Seiberg-Witten Theory
Graduate Studies in Mathematics, Vol. 28, (2000)
https://www3.nd.edu/~lnicolae/swnotes.pdf

Michael Hutchings and Clifford Henry Taubes,
An introduction to the Seiberg-Witten
equations on symplectic manifolds
http://math.berkeley.edu/~hutching/pub/tn.pdf