Equivariant Weiss Calculus

Prasit Bhattacharya; Yang Hu

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arXiv · 2410.12087

Equivariant Weiss Calculus

Prasit Bhattacharya·Yang Hu

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Abstract

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.

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BibTeX RIS

Prasit Bhattacharya, Yang Hu. 2024-10-15. Equivariant Weiss Calculus. https://arxiv.org/abs/2410.12087

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