On the extension problems for three 33-stem homotopy groups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910514049712128 |
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| author | Yang, Juxin Wu, Jie |
| author_facet | Yang, Juxin Wu, Jie |
| contents | This paper tackles the extension problems for three far-unsatble homotopy groups $π_{39}(S^{6})$, $π_{40}(S^{7})$, and $π_{41}(S^{8})$ localized at 2, the puzzles having remained unsolved for forty-five years. By a Toda bracket indexed by 1 included in $π_{39}(S^{6}_{(2)})$, which makes better use of the deuspension property of homotopy classes, we address the problems. As a corollary, through Thomeier's 8-step backward theorem of the metastable homotopy theory, together with the results of Oda, Mukai and Miyauchi, we show a table of the 33-stem homotopy groups $π_{33+n}(S^{n}_{(2)})$, ($2\leq n\leq 9$, $n\geq27$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08621 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the extension problems for three 33-stem homotopy groups Yang, Juxin Wu, Jie Algebraic Topology This paper tackles the extension problems for three far-unsatble homotopy groups $π_{39}(S^{6})$, $π_{40}(S^{7})$, and $π_{41}(S^{8})$ localized at 2, the puzzles having remained unsolved for forty-five years. By a Toda bracket indexed by 1 included in $π_{39}(S^{6}_{(2)})$, which makes better use of the deuspension property of homotopy classes, we address the problems. As a corollary, through Thomeier's 8-step backward theorem of the metastable homotopy theory, together with the results of Oda, Mukai and Miyauchi, we show a table of the 33-stem homotopy groups $π_{33+n}(S^{n}_{(2)})$, ($2\leq n\leq 9$, $n\geq27$). |
| title | On the extension problems for three 33-stem homotopy groups |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2406.08621 |