Tunisian Journal of Mathematics

The cohomology of $C_2$-equivariant $\mathcal{A}(1)$ and the homotopy of $ko_{C_2}$

Bertrand J. Guillou, Michael A. Hill, Daniel C. Isaksen, and Douglas Conner Ravenel

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Abstract

We compute the cohomology of the subalgebra A C 2 ( 1 ) of the C 2 -equivariant Steenrod algebra A C 2 . This serves as the input to the C 2 -equivariant Adams spectral sequence converging to the completed RO ( C 2 ) -graded homotopy groups of an equivariant spectrum ko C 2 . Our approach is to use simpler -motivic and -motivic calculations as stepping stones.

Article information

Source
Tunisian J. Math., Volume 2, Number 3 (2020), 567-632.

Dates
Received: 12 December 2018
Revised: 15 July 2019
Accepted: 30 July 2019
First available in Project Euclid: 13 December 2019

Permanent link to this document
https://projecteuclid.org/euclid.tunis/1576206290

Digital Object Identifier
doi:10.2140/tunis.2020.2.567

Mathematical Reviews number (MathSciNet)
MR4041284

Subjects
Primary: 14F42: Motivic cohomology; motivic homotopy theory [See also 19E15] 55Q91: Equivariant homotopy groups [See also 19L47] 55T15: Adams spectral sequences

Keywords
Adams spectral sequence motivic homotopy equivariant homotopy equivariant K-theory cohomology of the Steenrod algebra

Citation

Guillou, Bertrand J.; Hill, Michael A.; Isaksen, Daniel C.; Ravenel, Douglas Conner. The cohomology of $C_2$-equivariant $\mathcal{A}(1)$ and the homotopy of $ko_{C_2}$. Tunisian J. Math. 2 (2020), no. 3, 567--632. doi:10.2140/tunis.2020.2.567. https://projecteuclid.org/euclid.tunis/1576206290


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