Circle actions on oriented 4-manifolds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911556792483840 |
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| author | Jang, Donghoon Musin, Oleg R. |
| author_facet | Jang, Donghoon Musin, Oleg R. |
| contents | In the present paper, we consider an action of the circle group on a compact oriented 4-manifold. We derive the Atiyah-Hirzebruch formula for the manifold, and associate a graph in terms of data on the fixed point set. We show in the case of isolated fixed points that if an abstract graph satisfies the Atiyah-Hirzebruch formula, then there exists a corresponding 4-dimensional oriented $S^1$-manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_04576 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Circle actions on oriented 4-manifolds Jang, Donghoon Musin, Oleg R. Algebraic Topology Combinatorics Geometric Topology In the present paper, we consider an action of the circle group on a compact oriented 4-manifold. We derive the Atiyah-Hirzebruch formula for the manifold, and associate a graph in terms of data on the fixed point set. We show in the case of isolated fixed points that if an abstract graph satisfies the Atiyah-Hirzebruch formula, then there exists a corresponding 4-dimensional oriented $S^1$-manifold. |
| title | Circle actions on oriented 4-manifolds |
| topic | Algebraic Topology Combinatorics Geometric Topology |
| url | https://arxiv.org/abs/2307.04576 |