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Title:
Finite-energy SW monopoles on Cx∑
Speaker:
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 their dimensional reduction in dimension 3, Kronheimer–Mrowka defined monopole Floer homology for any closed 3-manifold. In this talk, we continue this reduction process and consider the moduli space of solutions on X = C × Σ, where Σ 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 to compact 3-manifolds with boundary, and this work can be viewed as the first step towards this goal.
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