The cohomology of c2-equivariant a(1) and the homotopy of koc2

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

doi:10.2140/tunis.2020.2.567

The cohomology of c₂-equivariant a(1) and the homotopy of ko_c2

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

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

We compute the cohomology of the subalgebra A^C2(1) of the C₂-equivariant Steenrod algebra A^C2. 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 ko_C2 . Our approach is to use simpler ℂ-motivic and ℝ-motivic calculations as stepping stones.

Original language	English (US)
Pages (from-to)	567-632
Number of pages	66
Journal	Tunisian Journal of Mathematics
Volume	2
Issue number	3
DOIs	https://doi.org/10.2140/tunis.2020.2.567
State	Published - 2020
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2020, Mathematical Science Publishers. All rights reserved.

Keywords

Adams spectral sequence
Cohomology of the Steenrod algebra
Equivariant K-theory
Equivariant homotopy
Motivic homotopy

Publisher link

10.2140/tunis.2020.2.567

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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 ℂ-motivic and ℝ-motivic calculations as stepping stones.",

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AU - Isaksen, Daniel C.

AU - Ravenel, Douglas Conner

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AB - 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 ℂ-motivic and ℝ-motivic calculations as stepping stones.

KW - Adams spectral sequence

KW - Cohomology of the Steenrod algebra

KW - Equivariant K-theory

KW - Equivariant homotopy

KW - Motivic homotopy

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