From Maxwell's Equations To Donaldson's Theory

The reinterpretation of the classical Maxwell's equations in terms of differential forms naturally leads to the attempt of generalizing the Maxwell's equations to more general settings aiming to unify the three fundamental forces including electromagnetic force,strong force and weak force beyond gravity.This is the content of Yang-Mills theory.However,the generalized Maxwell's equations-Yang-Mills equations not only reflect the physical laws of particles' behaviors,but also catch deep geometrical and topological information about the base manifold.Donaldson has extracted many information about four manifolds by analyzing the shape of the moduli space of self-dual connections under gauge equivalence on SU(2)-bundles over a compact oriented simply connected smooth four manifolds.This thesis exhibits Donaldson's creative work with author's own interpretations.