$C_2$-Equivariant Orthogonal Calculus
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916593315872768 |
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| author | Yavuz, Emel |
| author_facet | Yavuz, Emel |
| contents | In this paper, we construct a version of orthogonal calculus for functors from $C_2$-representations to $C_2$-spaces, where $C_2$ is the cyclic group of order 2. For example, the functor $BO(-)$, that sends a $C_2$-representation to the classifying space of its orthogonal group, which has a $C_2$-action induced by the action on the $C_2$-representation. We obtain a bigraded sequence of approximations to such a functor, and via a zig-zag of Quillen equivalences, we prove that the homotopy fibres of maps between approximations are fully determined by orthogonal spectra with a genuine action of $C_2$ and a naive action of the orthogonal group $O(p,q):=O(\mathbb{R}^{p+qδ})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_14077 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $C_2$-Equivariant Orthogonal Calculus Yavuz, Emel Algebraic Topology 55P42, 55P91, 55U35 In this paper, we construct a version of orthogonal calculus for functors from $C_2$-representations to $C_2$-spaces, where $C_2$ is the cyclic group of order 2. For example, the functor $BO(-)$, that sends a $C_2$-representation to the classifying space of its orthogonal group, which has a $C_2$-action induced by the action on the $C_2$-representation. We obtain a bigraded sequence of approximations to such a functor, and via a zig-zag of Quillen equivalences, we prove that the homotopy fibres of maps between approximations are fully determined by orthogonal spectra with a genuine action of $C_2$ and a naive action of the orthogonal group $O(p,q):=O(\mathbb{R}^{p+qδ})$. |
| title | $C_2$-Equivariant Orthogonal Calculus |
| topic | Algebraic Topology 55P42, 55P91, 55U35 |
| url | https://arxiv.org/abs/2501.14077 |