The stable homotopy theory of vortices on Riemann surfaces

2013/10/29 by Markus Szymik, Szymik, Markus
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1310.7737

openalex publication_date 2013/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of these notes is to show that the methods introduced by Bauer and Furuta in order to refine the Seiberg-Witten invariants of smooth 4-dimensional manifolds can also be used to obtain stable homotopy classes from Riemann surfaces, using the vortex equations on the latter.

Citations

• The Self-Duality Equations on a Riemann Surface
• Non-abelian monopoles and vortices
• ArbitraryN-vortex solutions to the first order Ginzburg-Landau equations

Related

• Vortices on surfaces with cylindrical ends
• The Coupled Seiberg-Witten Equations, vortices, and Moduli spaces of stable pairs
• The role of homology in fluid vortices I: non-relativistic flow
• Non-abelian monopoles and vortices
• A stable cohomotopy refinement of Seiberg-Witten invariants: II