On the closed geodesics problem
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
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| _version_ | 1866917337318293504 |
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| author | Ndombol, Bitjong |
| author_facet | Ndombol, Bitjong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18926 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the closed geodesics problem Ndombol, Bitjong Algebraic Topology 16E40 (primary) 16E45, 55P35, 55Pxx, 57T30, 57T05 (secondary) 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. |
| title | On the closed geodesics problem |
| topic | Algebraic Topology 16E40 (primary) 16E45, 55P35, 55Pxx, 57T30, 57T05 (secondary) |
| url | https://arxiv.org/abs/2602.18926 |