The Rational Homotopy of Stable $C_p$-Smoothings
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914414058274816 |
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| author | Wang, Oliver H. |
| author_facet | Wang, Oliver H. |
| contents | Smooth structures on high dimensional manifolds are classified by maps to the infinite loop space $TOP/O$. The homotopy groups of this space are known to be finite. Given a compact Lie group $G$, this space can be regarded as an equivariant infinite loop space and equivariant maps from a locally linear, high dimensional $G$-manifold to $TOP/O$ classify stable $G$-smoothings. We compute the equivariant homotopy groups $π_V^{C_p}TOP/O\otimes\mathbb{Q}$ where $C_p$ denotes the cyclic group of order $p$. By applying our methods to the group $C_4$, we prove a Chern class analogue of Novikov's theorem on rational Pontryagin classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11622 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Rational Homotopy of Stable $C_p$-Smoothings Wang, Oliver H. Algebraic Topology Geometric Topology Smooth structures on high dimensional manifolds are classified by maps to the infinite loop space $TOP/O$. The homotopy groups of this space are known to be finite. Given a compact Lie group $G$, this space can be regarded as an equivariant infinite loop space and equivariant maps from a locally linear, high dimensional $G$-manifold to $TOP/O$ classify stable $G$-smoothings. We compute the equivariant homotopy groups $π_V^{C_p}TOP/O\otimes\mathbb{Q}$ where $C_p$ denotes the cyclic group of order $p$. By applying our methods to the group $C_4$, we prove a Chern class analogue of Novikov's theorem on rational Pontryagin classes. |
| title | The Rational Homotopy of Stable $C_p$-Smoothings |
| topic | Algebraic Topology Geometric Topology |
| url | https://arxiv.org/abs/2510.11622 |