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arXiv · 1904.11237

Qualitative counting closed geodesics

Bastien Karlhofer·Jarek Kędra·Michał Marcinkowski·Alexander Trost
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Abstract

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.

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Bastien Karlhofer, Jarek Kędra, Michał Marcinkowski, Alexander Trost. 2019-04-25. Qualitative counting closed geodesics. https://doi.org/10.1007/s10711-021-00595-1

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