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arXiv · 2407.18537

Non-existence of an Algorithm for Determining the Triviality of the Second Homotopy Groups of Arbitrary Compact Topological Spaces

Lefit Yuxiang Hao·Zijie Kang·Hongjie Liu·Pengcheng Ma·Mufeng Zhou
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Abstract

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.

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Lefit Yuxiang Hao, Zijie Kang, Hongjie Liu, Pengcheng Ma, Mufeng Zhou. 2024-07-26. Non-existence of an Algorithm for Determining the Triviality of the Second Homotopy Groups of Arbitrary Compact Topological Spaces. https://arxiv.org/abs/2407.18537

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