Japanese Journal of Mathematics

, Volume 10, Issue 2, pp 105–133 | Cite as

Floer theory and its topological applications

Takagi Lectures


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.

Keywords and phrases

Floer homology Yang–Mills Seiberg–Witten homology cobordism triangulations 

Mathematics Subject Classification (2010)

57R58 (primary) 57M25 57M27 (secondary) 


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Copyright information

© The Mathematical Society of Japan and Springer Japan 2015

Authors and Affiliations

  1. 1.Department of MathematicsUCLALos AngelesUSA

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