Whitehead doubling, rank estimate and nonembeddability of contractible open manifolds
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916996021485568 |
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| author | Gu, Shijie Wang, Jian Zou, Yanqing |
| author_facet | Gu, Shijie Wang, Jian Zou, Yanqing |
| contents | Let $K$ be a nontrivial knot. For each $n\in \mathbb{N}$, we prove that the rank of its $n$th iterated Whitehead doubled knot group $π_1(S^3 \setminus \operatorname{WD}^n(K))$ is bounded below by $n+1$. As an application, we show that there exist infinitely many non-homeomorphic contractible open $n$-manifolds ($n\geq 3$) which cannot embed in a compact, locally connected and locally 1-connected $n$-dimensional metric space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06598 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Whitehead doubling, rank estimate and nonembeddability of contractible open manifolds Gu, Shijie Wang, Jian Zou, Yanqing Geometric Topology General Topology Group Theory Let $K$ be a nontrivial knot. For each $n\in \mathbb{N}$, we prove that the rank of its $n$th iterated Whitehead doubled knot group $π_1(S^3 \setminus \operatorname{WD}^n(K))$ is bounded below by $n+1$. As an application, we show that there exist infinitely many non-homeomorphic contractible open $n$-manifolds ($n\geq 3$) which cannot embed in a compact, locally connected and locally 1-connected $n$-dimensional metric space. |
| title | Whitehead doubling, rank estimate and nonembeddability of contractible open manifolds |
| topic | Geometric Topology General Topology Group Theory |
| url | https://arxiv.org/abs/2510.06598 |