Qualitative counting closed geodesics

Bastien Karlhofer, Jarek Kędra* (Corresponding Author), Michał Marcinkowski, Alexander Trost

*Corresponding author for this work

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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.
Original languageEnglish
Pages (from-to)523-530
JournalGeometriae Dedicata
Early online date28 Jan 2021
Publication statusPublished - 31 Aug 2021

Bibliographical note

Open Access via the Springer Compact Agreement

Acknowledgements This work was partly funded by the Leverhulme Trust Research Project Grant RPG-2017-159. MM is supported by the grant Sonatina 2018/28/C/ST1/00542 funded by Narodowe Centrum Nauki. MM and JK were partially supported by SFB 1085 “Higher Invariants” funded by Deutsche Forschungsgemeinschaft.


  • math.DG
  • math.GR
  • math.GT


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