Vol. 2, No. 3, 2020

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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

Vol. 2 (2020), No. 3, 567–632
Abstract

We compute the cohomology of the subalgebra AC2(1) of the C2-equivariant Steenrod algebra AC2. This serves as the input to the C2-equivariant Adams spectral sequence converging to the completed RO(C2)-graded homotopy groups of an equivariant spectrum koC2. Our approach is to use simpler -motivic and -motivic calculations as stepping stones.

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Keywords
Adams spectral sequence, motivic homotopy, equivariant homotopy, equivariant K-theory, cohomology of the Steenrod algebra
Mathematical Subject Classification 2010
Primary: 14F42, 55Q91, 55T15
Milestones
Received: 12 December 2018
Revised: 15 July 2019
Accepted: 30 July 2019
Published: 9 October 2019
Authors
Bertrand J. Guillou
Department of Mathematics
The University of Kentucky
Lexington, KY
United States
Michael A. Hill
Department of Mathematics
University of California
Los Angeles, CA
United States
Daniel C. Isaksen
Department of Mathematics
Wayne State University
Detroit, MI
United States
Douglas Conner Ravenel
Department of Mathematics
University of Rochester
NY
United States