English

Floer theory and its topological applications

Geometric Topology 2015-08-04 v1 Differential Geometry Symplectic Geometry

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.

Keywords

Cite

@article{arxiv.1508.00495,
  title  = {Floer theory and its topological applications},
  author = {Ciprian Manolescu},
  journal= {arXiv preprint arXiv:1508.00495},
  year   = {2015}
}

Comments

Notes based on the 14th Takagi Lectures at the University of Tokyo; to appear in the Japanese Journal of Mathematics

R2 v1 2026-06-22T10:25:13.959Z