Adiabatic limits of Seiberg-Witten equations on Seifert manifolds

TL;DR

This paper provides a simplified proof for the existence of adiabatic limits of Seiberg-Witten equations on Seifert manifolds and explores reversing the adiabatic process to obtain genuine solutions.

Contribution

It introduces a simpler proof for adiabatic limits and demonstrates how to deform these limits into irreducible solutions in certain cases.

Findings

Simplified proof for existence of adiabatic limits

Reversal of adiabatic process to find genuine solutions

Deformation of limits into irreducible solutions in nondegenerate cases

Abstract

We present a simpler proof for the existence of adiabatic limits. Moreover, we added a new section where the adiabatic process is reversed and in some nondegenerate cases we deform the adiabatic limits to genuine irreducible solutions of the SW equations.