The relative James construction and its application to homotopy groups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915007978012672 |
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| author | Zhu, Zhongjian Jin, Tian |
| author_facet | Zhu, Zhongjian Jin, Tian |
| contents | In this paper, we develop the new method to compute the homotopy groups of the mapping cone $C_f=Y\cup_{f}CX$ beyond the metastable range by analysing the homotopy of the $n$-th filtration of the relative James construction $J(X,A)$ for CW-pair $A\stackrel{i}\hookrightarrow X$, defined by B. Gray, which is homotopy equivalent to the homotopy fiber of the pinch map $X\cup_{i}CA\rightarrow ΣA$. As an application, we compute the 5 and 6-dim unstable homotopy groups of 3-dimensional mod $2^r$ Moore spaces for all positive integers $r$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07072 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The relative James construction and its application to homotopy groups Zhu, Zhongjian Jin, Tian Algebraic Topology In this paper, we develop the new method to compute the homotopy groups of the mapping cone $C_f=Y\cup_{f}CX$ beyond the metastable range by analysing the homotopy of the $n$-th filtration of the relative James construction $J(X,A)$ for CW-pair $A\stackrel{i}\hookrightarrow X$, defined by B. Gray, which is homotopy equivalent to the homotopy fiber of the pinch map $X\cup_{i}CA\rightarrow ΣA$. As an application, we compute the 5 and 6-dim unstable homotopy groups of 3-dimensional mod $2^r$ Moore spaces for all positive integers $r$. |
| title | The relative James construction and its application to homotopy groups |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2402.07072 |