Japanese Journal of Mathematics

, Volume 10, Issue 2, pp 105–133

Floer theory and its topological applications

Takagi Lectures

DOI: 10.1007/s11537-015-1487-8

Cite this article as:
Manolescu, C. Jpn. J. Math. (2015) 10: 105. doi:10.1007/s11537-015-1487-8


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) 

Copyright information

© The Mathematical Society of Japan and Springer Japan 2015

Authors and Affiliations

  1. 1.Department of MathematicsUCLALos AngelesUSA