Realization of manifolds as leaves using graph colorings

Realization of manifolds as leaves using graph colorings

It is proved that any (repetitive) Riemannian manifold of bounded geometry can be realized as a leaf of some (minimal) Riemannian matchbox manifold without holonomy. Our methods can be adapted to achieve Cantor transversals or a prescribed holonomy covering, but then the manifold may not be realized...

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Hauptverfasser: López, Jesús A. Álvarez, Lijó, Ramón Barral
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Dynamical Systems
Mathematics - Geometric Topology
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Beschreibung
Zusammenfassung:It is proved that any (repetitive) Riemannian manifold of bounded geometry can be realized as a leaf of some (minimal) Riemannian matchbox manifold without holonomy. Our methods can be adapted to achieve Cantor transversals or a prescribed holonomy covering, but then the manifold may not be realized as a dense leaf.
DOI:10.48550/arxiv.2002.08662