Qualitative counting closed geodesics

Qualitative counting closed geodesics

We investigate the geometry of word metrics on fundamental groups of manifolds associated with the generating sets consisting of elements represented by closed geodesics. We ask whether the diameter of such a metric is finite or infinite. The first answer we interpret as an abundance of closed geode...

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Veröffentlicht in:Geometriae dedicata 2021-08, Vol.213 (1), p.523-530
Hauptverfasser: Karlhofer, Bastien, Kędra, Jarek, Marcinkowski, Michał, Trost, Alexander
Format: Artikel
Sprache:eng
Schlagworte:
Algebraic Geometry
Convex and Discrete Geometry
Differential Geometry
Geodesy
Hyperbolic Geometry
Mathematics
Mathematics and Statistics
Original Paper
Projective Geometry
Topology
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Zusammenfassung:We investigate the geometry of word metrics on fundamental groups of manifolds associated with the generating sets consisting of elements represented by closed geodesics. We ask whether the diameter of such a metric is finite or infinite. The first answer we interpret as an abundance of closed geodesics, while the second one as their scarcity. We discuss examples for both cases.
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-021-00595-1