On the Classification of $S^3$-Bundles over $\mathbb{C}P^2$
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917115314831360 |
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| author | Liu, Wancheng |
| author_facet | Liu, Wancheng |
| contents | This paper presents a classification of the total spaces of $S^3$-bundles over $\mathbb{C}P^2$ up to orientation-preserving homotopy equivalence. Our approach proceeds in two steps: we first derive the PL-homeomorphism classification for these manifolds by computing their Kreck-Stolz invariants. Then, building upon this PL classification result and through an application of surgery theory, we establish the homotopy equivalence classification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22999 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Classification of $S^3$-Bundles over $\mathbb{C}P^2$ Liu, Wancheng Algebraic Topology Geometric Topology This paper presents a classification of the total spaces of $S^3$-bundles over $\mathbb{C}P^2$ up to orientation-preserving homotopy equivalence. Our approach proceeds in two steps: we first derive the PL-homeomorphism classification for these manifolds by computing their Kreck-Stolz invariants. Then, building upon this PL classification result and through an application of surgery theory, we establish the homotopy equivalence classification. |
| title | On the Classification of $S^3$-Bundles over $\mathbb{C}P^2$ |
| topic | Algebraic Topology Geometric Topology |
| url | https://arxiv.org/abs/2511.22999 |