Homotopy exponents of polyhedral products
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914547504250880 |
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| author | Eldridge, Briony |
| author_facet | Eldridge, Briony |
| contents | We study Moore's conjecture and homotopy exponents for polyhedral products. For $(\underline{CA},\underline{A})^K$ where each $A_i$ is finite and has torsion-free homology, we prove that if $(\underline{CA},\underline{A})^K$ is rationally hyperbolic, then it has no homotopy exponent at any odd prime. Under the additional hypothesis $ΣA_i$ is homotopy equivalent to a finite-type wedge of simply-connected spheres, we show Moore's conjecture holds for $(\underline{CA},\underline{A})^K$. We also give criteria such that, for a large family of polyhedral join products, the associated polyhedral products are rationally hyperbolic, mod-$p^r$ hyperbolic for all but finitely many primes, and have no homotopy exponent at all but finitely many primes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08707 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Homotopy exponents of polyhedral products Eldridge, Briony Algebraic Topology Primary 55Q05, Secondary 55P62, 55U10 We study Moore's conjecture and homotopy exponents for polyhedral products. For $(\underline{CA},\underline{A})^K$ where each $A_i$ is finite and has torsion-free homology, we prove that if $(\underline{CA},\underline{A})^K$ is rationally hyperbolic, then it has no homotopy exponent at any odd prime. Under the additional hypothesis $ΣA_i$ is homotopy equivalent to a finite-type wedge of simply-connected spheres, we show Moore's conjecture holds for $(\underline{CA},\underline{A})^K$. We also give criteria such that, for a large family of polyhedral join products, the associated polyhedral products are rationally hyperbolic, mod-$p^r$ hyperbolic for all but finitely many primes, and have no homotopy exponent at all but finitely many primes. |
| title | Homotopy exponents of polyhedral products |
| topic | Algebraic Topology Primary 55Q05, Secondary 55P62, 55U10 |
| url | https://arxiv.org/abs/2605.08707 |