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| Главные авторы: | , |
|---|---|
| Формат: | Preprint |
| Опубликовано: |
2024
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| Предметы: | |
| Online-ссылка: | https://arxiv.org/abs/2406.08621 |
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Оглавление:
- 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 $π_{33+n}(S^{n}_{(2)})$, ($2\leq n\leq 9$, $n\geq27$).