Equivariant geometric bordism, representation, labelled graph
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909455367536640 |
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| author | Li, Hao Lü, Zhi Shen, Qifan |
| author_facet | Li, Hao Lü, Zhi Shen, Qifan |
| contents | This paper focuses on the following problem: {\em what $G_k$-representation polynomials in Conner--Floyd $G_k$-representation algebra arise as fixed point data of $G_k$-manifolds?}
where $G_k=(\mathbb{Z}_2)^k$.
Using the idea of the GKM theory, we construct a $G_k$-labelled graph from a smooth closed manifold with an effective $G_k$-action fixing a finite set. Then we give an answer to above mentioned problem through two approaches: $G_k$-labelled graphs and $G_k$-representation theory.
As an application, we give a complete classification of all 4-dimensional smooth closed manifolds with an effective $G_3$-action fixing a finite set up to equivariant unoriented bordism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06565 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivariant geometric bordism, representation, labelled graph Li, Hao Lü, Zhi Shen, Qifan Algebraic Topology 57R85, 05C22, 55M35, 57R91, 55N22 This paper focuses on the following problem: {\em what $G_k$-representation polynomials in Conner--Floyd $G_k$-representation algebra arise as fixed point data of $G_k$-manifolds?} where $G_k=(\mathbb{Z}_2)^k$. Using the idea of the GKM theory, we construct a $G_k$-labelled graph from a smooth closed manifold with an effective $G_k$-action fixing a finite set. Then we give an answer to above mentioned problem through two approaches: $G_k$-labelled graphs and $G_k$-representation theory. As an application, we give a complete classification of all 4-dimensional smooth closed manifolds with an effective $G_3$-action fixing a finite set up to equivariant unoriented bordism. |
| title | Equivariant geometric bordism, representation, labelled graph |
| topic | Algebraic Topology 57R85, 05C22, 55M35, 57R91, 55N22 |
| url | https://arxiv.org/abs/2501.06565 |