The singularities of Yang-Mills connections for bundles on a surface. II. The stratification
| dc.creator | Huebschmann, Johannes | |
| dc.date | 1994-11-22 | |
| dc.date.accessioned | 2026-07-07T09:12:27Z | |
| dc.date.available | 2026-07-07T09:12:27Z | |
| dc.description | Let $Σ$ be a closed surface, $G$ a compact Lie group, not necessarily connected, with Lie algebra $g$, endowed with an adjoint action invariant scalar product, let $ξ\colon P \to Σ$ be a principal $G$-bundle, and pick a Riemannian metric and orientation on $Σ$ so that the corresponding Yang-Mills equations are defined. In an earlier paper we determined the local structure of the moduli space $N(ξ)$ of central Yang-Mills connections on $ξ$ near an arbitrary point. Here we show that the decomposition of $N(ξ)$ into connected components of orbit types of central Yang-Mills connections is a stratification in the strong (i.~e. Whitney) sense; furthermore each stratum, being a smooth manifold, inherits a finite volume symplectic structure from the given data. This complements, in a way, results of {\smc Atiyah-Bott} in that it will in general decompose further the critical sets of the corresponding Yang-Mills functional into smooth pieces. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9411007 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9411007 | |
| dc.identifier | Math. Z. 221 (1996), 83-92 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152026 | |
| dc.subject | Differential Geometry | |
| dc.title | The singularities of Yang-Mills connections for bundles on a surface. II. The stratification | |
| dc.type | text |