Adiabatic limits of the Hermitian Yang-Mills equations on slicewise stable bundles
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A formal limit of the Hermitian Yang-Mills Equations on a SU(2) bundle over a product of two Riemann surfaces yields the Adiabatic Equations when the metric of the first surface is stretched ad infinitum. This thesis identifies the solutions of this new set of equations with holomorphic maps from the first surface into the moduli space of flat connections of the second one. Moreover, some advance is made in the study of the sort of bubbling phenomena that may occur when taking this limit. This dissertation is a step towards a rigorous proof of the relationship suggested by Bershadky, Johansen, Sadov and Vafa between Donaldson invariants and quantum cohomology, and relates to the program of Dostoglou and Salamon to prove the Atiyah-Floer conjecture.