Stratification of the Generalized Gauge Orbit Space

Details Stratification of the Generalized Gauge Orbit Space Stratification of the Generalized Gauge Orbit Space

2000-01-05

arxiv.org/abs/math-ph/0001008v1

Commun.Math.Phys. 214 (2000) 607-649

Physics

Mathematical Physics

LaTeX, 21 pages

Scientific paper

10.1007/s002200000286

The action of Ashtekar's generalized gauge group $\Gb$ on the space $\Ab$ of generalized connections is investigated for compact structure groups $\LG$. First a stratum is defined to be the set of all connections of one and the same gauge orbit type, i.e. the conjugacy class of the centralizer of the holonomy group. Then a slice theorem is proven on $\Ab$. This yields the openness of the strata. Afterwards, a denseness theorem is proven for the strata. Hence, $\Ab$ is topologically regularly stratified by $\Gb$. These results coincide with those of Kondracki and Rogulski for Sobolev connections. As a by-product, we prove that the set of all gauge orbit types equals the set of all (conjugacy classes of) Howe subgroups of $\LG$. Finally, we show that the set of all gauge orbits with maximal type has the full induced Haar measure 1.

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