2005/02/08 by Ronald J. Stern, Stern, Ronald J. · 1 citation
Computer Science · Mathematics · #14J26 #53D05 #57R55 #57R57 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #Topological and Geometric Data Analysis #math.GT #math.SG #msc:14J26 #msc:53D05 #msc:57R55 #msc:57R57
paper · pdf · doi:10.48550/arxiv.math/0502164
17 pages, 2004 Clay Institute Summer School on Floer homology, gauge theory, and low dimensional topology. More errata corrected
openalex publication_date 2005/02/08 · arxiv created 2005/02/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
These notes are adapted from two talks given at the 2004 Clay Institute Summer School on Floer homology, gauge theory, and low dimensional topology at the Alfred Renyi Institute. We will quickly review what we do and do not know about the existence and uniqueness of smooth and symplectic structures on closed, simply-connected 4-manifolds. We will then list the techniques used to date and capture the key features common to all these techniques. We finish with some approachable questions that further explore the relationship between these techniques and whose answers may assist in future advances towards a classification scheme.