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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
101/2002

Regular Connections among Generalized Connections

Christian Fleischhack

Abstract

The properties of the space $\cal A$ of regular connections as a subset of the space $\overline{\cal A}$ of generalized connections in the Ashtekar framework are studied. For every choice of compact structure group and smoothness category for the paths it is determined whether $\cal A$ is dense in $\overline{\cal A}$ or not. Moreover, it is proven that $\cal A$ has Ashtekar-Lewandowski measure zero for every nontrivial structure group and every smoothness category. The analogous results hold for gauge orbits instead of connections.

Received:
Nov 13, 2002
Published:
Nov 13, 2002
MSC Codes:
81T13, 53C05

Related publications

inJournal
2003 Repository Open Access
Christian Fleischhack

Regular connections among generalized connections

In: Journal of geometry and physics, 47 (2003) 4, pp. 469-483