On a Certain Stratification of the Gauge Orbit Space

2001/04/18 by Gerd Rudolph, G. Rudolph, Matthias Schmidt +3
Engineering · Mathematics · Physics and Astronomy · #53C05 #53C80 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Relativity and Gravitational Theory #Space Satellite Systems and Control #hep-th #math-ph #math.DG #math.MP #msc:53C05 #msc:53C80

paper · pdf · doi:10.48550/arxiv.math-ph/0104026

12 pages, 1 figure

arxiv created 2001/04/18 · openalex publication_date 2001/04/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a principal \rmSU(n)-bundle over a compact manifold of dimension 2,3,4, we determine the orbit types of the action of the gauge group on the space of connections modulo pointed local gauge transformations. We find that they are given by Howe subgroups of \rmSU(n) for which a certain characteristic equation is solvable. Depending on the base manifold, this equation leads to a linear, bilinear, or quadratic Diophantine equation.

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