February 19, 2018
4:00 PM - 5:00 PM
Math Tower 5-127
|David Hu, Stony Brook University|
The perturbed Seiberg-Witten moduli space
In general, the moduli space of solutions to the Seiberg-Witten equations modulo gauge equivalence may not be a smooth manifold. Two main problems arise when one tries to show smoothness using standard methods. The first is surjectivity of the differential of the Seiberg-Witten map. The second is the presence of reducible solutions (not only does the gauge group not act freely on such solutions, but it will turn out that first problem can only be solved if we restrict to irreducible solutions). In this talk we will show how both of these problems are resolved by introducing a perturbation to the Seiberg-Witten equations.