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Qualitative counting closed geodesics (1904.11237v2)
Published 25 Apr 2019 in math.DG, math.GR, and math.GT
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.