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Floer theory and its topological applications (1508.00495v1)
Published 3 Aug 2015 in math.GT, math.DG, and math.SG
Abstract: We survey the different versions of Floer homology that can be associated to three-manifolds. We also discuss their applications, particularly to questions about surgery, homology cobordism, and four-manifolds with boundary. We then describe Floer stable homotopy types, the related Pin(2)-equivariant Seiberg-Witten Floer homology, and its application to the triangulation conjecture.
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