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arXiv · 2004.00806

The $C_2$-effective spectral sequence for $C_2$-equivariant connective real $K$-theory

Hana Jia Kong
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Abstract

We construct a $C_2$-equivariant spectral sequence for RO$(C_2)$-graded homotopy groups. The construction is by using the motivic effective slice filtration and the $C_2$-equivariant Betti realization. We apply the spectral sequence to compute the RO$(C_2)$-graded homotopy groups of the completed $C_2$-equivariant connective real $K$-theory spectrum. The computation reproves the $C_2$-equivariant Adams spectral sequence results by Guillou, Hill, Isaksen and Ravenel.

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BibTeXRIS

Hana Jia Kong. 2020-04-02. The $C_2$-effective spectral sequence for $C_2$-equivariant connective real $K$-theory. https://doi.org/10.2140/tunis.2023.5.627

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