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 |
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| container_title | Geometriae dedicata |
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| creator | Karlhofer, Bastien Kędra, Jarek Marcinkowski, Michał Trost, Alexander |
| description | 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. |
| doi_str_mv | 10.1007/s10711-021-00595-1 |
| format | Article |
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| subjects | Algebraic Geometry Convex and Discrete Geometry Differential Geometry Geodesy Hyperbolic Geometry Mathematics Mathematics and Statistics Original Paper Projective Geometry Topology |
| title | Qualitative counting closed geodesics |
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