Qualitative counting closed geodesics

Bastien Karlhofer; Jarek Kędra; Michał Marcinkowski; Alexander Trost

doi:10.1007/s10711-021-00595-1

Qualitative counting closed geodesics

Bastien Karlhofer, Jarek Kędra, Michał Marcinkowski, Alexander Trost

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	523-530
Number of pages	8
Journal	Geometriae Dedicata
Volume	213
Issue number	1
DOIs	https://doi.org/10.1007/s10711-021-00595-1
State	Published - 1 Aug 2021
Externally published	Yes

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s10711-021-00595-1

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Qualitative counting closed geodesics

Abstract

ASJC Scopus subject areas

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