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| Format: | Preprint |
| Published: |
2020
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| Online Access: | https://arxiv.org/abs/2008.00492 |
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| _version_ | 1866918274289106944 |
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| author | Skopenkov, A. |
| author_facet | Skopenkov, A. |
| contents | We present a short proof of the Čadek-Krčál-Matoušek-Vokřínek-Wagner result from the title (in the following form due to Filakovský-Wagner-Zhechev).
For any fixed even $l$ there is no algorithm recognizing the extendability of the identity map of $S^l$ to a PL map $X\to S^l$ of given $2l$-dimensional simplicial complex $X$ containing a subdivision of $S^l$ as a given subcomplex.
We also exhibit a gap in the Filakovský-Wagner-Zhechev proof that embeddability of complexes is undecidable in codimension $>1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_00492 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Extendability of simplicial maps is undecidable Skopenkov, A. Algebraic Topology Computational Geometry 55-02, 55P05, 55S36, 68-02, 68U05 We present a short proof of the Čadek-Krčál-Matoušek-Vokřínek-Wagner result from the title (in the following form due to Filakovský-Wagner-Zhechev). For any fixed even $l$ there is no algorithm recognizing the extendability of the identity map of $S^l$ to a PL map $X\to S^l$ of given $2l$-dimensional simplicial complex $X$ containing a subdivision of $S^l$ as a given subcomplex. We also exhibit a gap in the Filakovský-Wagner-Zhechev proof that embeddability of complexes is undecidable in codimension $>1$. |
| title | Extendability of simplicial maps is undecidable |
| topic | Algebraic Topology Computational Geometry 55-02, 55P05, 55S36, 68-02, 68U05 |
| url | https://arxiv.org/abs/2008.00492 |