2005/01/06 by Daniel Ruberman, Ruberman, Daniel, Nikolai Saveliev +1
Computer Science · Mathematics · #57M27 #57R58 #58D27 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.GT #msc:57M27 #msc:57R58 #msc:58D27
paper · pdf · doi:10.48550/arxiv.math/0501090
30 pages, 5 figures. To appear in Proceedings of the Fields-McMaster Conference on Geometry and Topology of Manifolds
arxiv created 2005/01/06 · openalex publication_date 2005/01/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article surveys our ongoing project about the relationship between invariants extending the classical Rohlin invariant of homology spheres and those coming from 4-dimensional (Yang-Mills) gauge theory. The main conjecture towards which this project is directed is that the Rohlin invariant and the gauge theoretic invariant coincide for a homology S1× S3. We discuss the implications of this conjecture for some classical problems in low-dimensional topology, and progress we have made towards proving the conjecture.