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arXiv · 2307.13877

Remark on non-contractible closed geodesics and homotopy groups

Egor Shelukhin·Jun Zhang
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Abstract

We prove that if the $m$-th homotopy group for $m \geq 2$ of a closed manifold has non-trivial invariants or coinvariants under the action of the fundamental group, then there exist infinitely many geometrically distinct closed geodesics for a $C^4$-generic Riemannian metric. If moreover there are infinitely many conjugacy classes in the fundamental group, then the same holds for every Riemannian metric.

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Egor Shelukhin, Jun Zhang. 2023-07-26. Remark on non-contractible closed geodesics and homotopy groups. https://arxiv.org/abs/2307.13877

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