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Gauge Theory Learning Seminar

Heegaard Floer homology and the Thom conjecture

Isabella Khan (Princeton University)

Location:  Hill 705 and Zoom
Date & time: Tuesday, 20 February 2024 at 12:00PM - 1:00PM

Abstract: The Heegaard Floer invariants associate to a given three manifold an Abelian group in such a way as to retrieve important information about the underlying manifold. To illustrate this, as well as some of the interesting aspects of the construction itself, we will discuss the Heegaard Floer homology proof of the Thom conjecture for CP^2 (first resolved by Kronheimer and Mrowka in 1994, using Seiberg-Witten invariants). This expository talk will be based on the 2002 paper "Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary" of Ozsváth and Szabó, as well as several other contemporary articles.