Equivariant bordism classification of five-dimensional $(\mathbb{Z}_2)^3$-manifolds with isolated fixed points
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916688483581952 |
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| author | Guan, Yuanxin Lü, Zhi |
| author_facet | Guan, Yuanxin Lü, Zhi |
| contents | Denote by $\mathcal{Z}_5((\mathbb{Z}_2)^3)$ the group, which is also a vector space over $\mathbb{Z}_2$, generated by equivariant unoriented bordism classes of all five-dimensional closed smooth manifolds with effective smooth $(\mathbb{Z}_2)^3$-actions fixing isolated points. We show that $\dim_{\mathbb{Z}_2} \mathcal{Z}_5((\mathbb{Z}_2)^3) = 77$ and determine a basis of $\mathcal{Z}_5((\mathbb{Z}_2)^3)$, each of which is explicitly chosen as the projectivization of a real vector bundle. Thus this gives a complete classification up to equivariant unoriented bordism of all five-dimensional closed smooth manifolds with effective smooth $(\mathbb{Z}_2)^3$-actions with isolated fixed points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09988 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivariant bordism classification of five-dimensional $(\mathbb{Z}_2)^3$-manifolds with isolated fixed points Guan, Yuanxin Lü, Zhi Algebraic Topology Denote by $\mathcal{Z}_5((\mathbb{Z}_2)^3)$ the group, which is also a vector space over $\mathbb{Z}_2$, generated by equivariant unoriented bordism classes of all five-dimensional closed smooth manifolds with effective smooth $(\mathbb{Z}_2)^3$-actions fixing isolated points. We show that $\dim_{\mathbb{Z}_2} \mathcal{Z}_5((\mathbb{Z}_2)^3) = 77$ and determine a basis of $\mathcal{Z}_5((\mathbb{Z}_2)^3)$, each of which is explicitly chosen as the projectivization of a real vector bundle. Thus this gives a complete classification up to equivariant unoriented bordism of all five-dimensional closed smooth manifolds with effective smooth $(\mathbb{Z}_2)^3$-actions with isolated fixed points. |
| title | Equivariant bordism classification of five-dimensional $(\mathbb{Z}_2)^3$-manifolds with isolated fixed points |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2504.09988 |