The $RO(C_{2^n})$-graded homotopy of $H\underline{\mathbb{Z}}$ through generalized Tate squares

Guoqi Yan

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arXiv · 2208.14368

The $RO(C_{2^n})$-graded homotopy of $H\underline{\mathbb{Z}}$ through generalized Tate squares

Guoqi Yan

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Abstract

We propose a new method to compute the $C_{2^n}$-equivariant homotopy groups of the Eilenberg-Mac Lane spectrum $H\underline{\mathbb{Z}}$ as a $RO(C_{2^n})$-graded Green functor using the generalized Tate squares. As an example, we completely compute the $C_4$ case and investigate two $\mathscr{P}$-homotopy limit spectral sequences for the family $\mathscr{P}=\{e,C_2\}$.

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BibTeX RIS

Guoqi Yan. 2022-08-30. The $RO(C_{2^n})$-graded homotopy of $H\underline{\mathbb{Z}}$ through generalized Tate squares. https://arxiv.org/abs/2208.14368

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