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Hyphs and the Ashtekar-Lewandowski measure
Christian FleischhackAbstract
Properties of the space
First a construction method for new connections is given. The new parallel transports differ from the original ones only along paths that pass an initial segment of a fixed path. This is closely related to a new notion of path independence. Although we do not restrict ourselves to the immersive smooth or analytical case, any finite set of paths depends on a finite set of independent paths, a so-called hyph. This generalizes the well-known directedness of the set of smooth webs and that of analytical graphs, respectively.
Due to these propositions, on the one hand, the projections from
- Received:
- 27.01.00
- Published:
- 27.01.00