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arXiv · 2602.18926

On the closed geodesics problem

Bitjong Ndombol
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Abstract

Let $\bk $ be a field of characteristic $p\geq 0$ and $X$ a simply connected finite CW complex. In this text, we prove that: {\sl if the cohomology algebra $H^*(X;\bk)$ is generated, as an algebra, by at least two linearly independent elements, then the sequence of Betti numbers $ \left( \dim H^n(LX;\bk)\right)_{n\geq 1 }$ grows unbounded.} This provides a complete solution of the closed geodesics problem.

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Bitjong Ndombol. 2026-02-21. On the closed geodesics problem. https://arxiv.org/abs/2602.18926

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