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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Abstract:
The action of Ashtekar's generalized gauge group on the space of generalized connections is investigated for compact structure groups . 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 . This yields the openness of the strata. Afterwards, a denseness theorem is proven for the strata. Hence, is topologically regularly stratified by . 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 . Finally, we show that the set of all gauge orbits with maximal type has the full induced Haar measure 1.