Geometry Seminar

Date: October 21, 2019

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Donghao Wang, MIT

Title: Finite Energy Monopoles on $\C \times \Sigma$

Abstract: The Seiberg-Witten (monopole) equations and the monopole invariants introduced by Witten have greatly influenced the study of smooth 4-manifolds since 1994. By studying its dimensional reduction in dimension 3, Kronheimer-Mrowka defined the monopole Floer homology for any closed 3-manifolds. In this talk, we continue this reduction process and consider the moduli space of solutions on $X=\mathbb{C}\times\Sigma$, where $\Sigma$ is a compact Riemann surface. We will classify solutions to the Seiberg-Witten equations on $X$ with finite analytic energy and estimate their decay rates at infinity according to the algebraic input. The motivation is to extend the construction of Kronheimer-Mrowka for compact 3-manifolds with boundary, and this work is the first step towards this goal.