Non-existence of an Algorithm for Determining the Triviality of the Second Homotopy Groups of Arbitrary Compact Topological Spaces
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914888353316864 |
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| author | Hao, Lefit Yuxiang Kang, Zijie Liu, Hongjie Ma, Pengcheng Zhou, Mufeng |
| author_facet | Hao, Lefit Yuxiang Kang, Zijie Liu, Hongjie Ma, Pengcheng Zhou, Mufeng |
| contents | In this paper, we demonstrate the non-existence of a computational algorithm capable of determining whether the second homotopy group of any compact constructive topological space is trivial. This finding shows the inherent limitations of computer methods in resolving certain topological problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18537 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-existence of an Algorithm for Determining the Triviality of the Second Homotopy Groups of Arbitrary Compact Topological Spaces Hao, Lefit Yuxiang Kang, Zijie Liu, Hongjie Ma, Pengcheng Zhou, Mufeng Algebraic Topology Optimization and Control In this paper, we demonstrate the non-existence of a computational algorithm capable of determining whether the second homotopy group of any compact constructive topological space is trivial. This finding shows the inherent limitations of computer methods in resolving certain topological problems. |
| title | Non-existence of an Algorithm for Determining the Triviality of the Second Homotopy Groups of Arbitrary Compact Topological Spaces |
| topic | Algebraic Topology Optimization and Control |
| url | https://arxiv.org/abs/2407.18537 |