Algorithmic aspects of immersibility and embeddability
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2018
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| _version_ | 1866908096691961856 |
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| author | Manin, Fedor Weinberger, Shmuel |
| author_facet | Manin, Fedor Weinberger, Shmuel |
| contents | We analyze an algorithmic question about immersion theory: for which $m$, $n$, and $CAT=\mathbf{Diff}$ or $\mathbf{PL}$ is the question of whether an $m$-dimensional $CAT$-manifold is immersible in $\mathbb{R}^n$ decidable? As a corollary, we show that the smooth embeddability of an $m$-manifold with boundary in $\mathbb{R}^n$ is undecidable when $n-m$ is even and $11m \geq 10n+1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1812_09413 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Algorithmic aspects of immersibility and embeddability Manin, Fedor Weinberger, Shmuel Geometric Topology Computational Geometry 57R42, 57Q35, 03D15 We analyze an algorithmic question about immersion theory: for which $m$, $n$, and $CAT=\mathbf{Diff}$ or $\mathbf{PL}$ is the question of whether an $m$-dimensional $CAT$-manifold is immersible in $\mathbb{R}^n$ decidable? As a corollary, we show that the smooth embeddability of an $m$-manifold with boundary in $\mathbb{R}^n$ is undecidable when $n-m$ is even and $11m \geq 10n+1$. |
| title | Algorithmic aspects of immersibility and embeddability |
| topic | Geometric Topology Computational Geometry 57R42, 57Q35, 03D15 |
| url | https://arxiv.org/abs/1812.09413 |