Equivariant Weiss Calculus
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914991790096384 |
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| author | Bhattacharya, Prasit Hu, Yang |
| author_facet | Bhattacharya, Prasit Hu, Yang |
| contents | In this paper, we introduce an equivariant analog of Weiss calculus of functors for all finite group $\mathrm{G}$. In our theory, Taylor approximations and derivatives are index by finite dimensional $\mathrm{G}$-representations, and homogeneous layers are classified by orthogonal $\mathrm{G}$-spectra. Further, our framework permits a notion of restriction as well as a notion of fixed-point at the level of Weiss functors. We establish various results comparing Taylor approximations and derivatives of fixed-point (resp. restrictions) functors to that of the fixed-point (resp. restrictions) of Taylor approximations and derivatives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12087 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivariant Weiss Calculus Bhattacharya, Prasit Hu, Yang Algebraic Topology 55P65, 55P91, 55P92 In this paper, we introduce an equivariant analog of Weiss calculus of functors for all finite group $\mathrm{G}$. In our theory, Taylor approximations and derivatives are index by finite dimensional $\mathrm{G}$-representations, and homogeneous layers are classified by orthogonal $\mathrm{G}$-spectra. Further, our framework permits a notion of restriction as well as a notion of fixed-point at the level of Weiss functors. We establish various results comparing Taylor approximations and derivatives of fixed-point (resp. restrictions) functors to that of the fixed-point (resp. restrictions) of Taylor approximations and derivatives. |
| title | Equivariant Weiss Calculus |
| topic | Algebraic Topology 55P65, 55P91, 55P92 |
| url | https://arxiv.org/abs/2410.12087 |