Preprint 4/2000

Stratification of the generalized gauge orbit space

Christian Fleischhack

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Submission date: 27. Jan. 2000
Pages: 29
published in: Communications in mathematical physics, 214 (2000) 3, p. 607-649 
DOI number (of the published article): 10.1007/s002200000286
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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.

24.11.2021, 02:11