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

Mathematics

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

16 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
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

Bibliographical note

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

Funding

The authors were supported by NSF grants DMS-1710379, DMS-1509652, DMS-1606290, and DMS-1606623 and by Simons Collaboration Grant No. 282316.

Funders	Funder number
Simons Collaboration	282316
National Science Foundation Arctic Social Science Program	1710379, 1509652, DMS-1606623, DMS-1606290, DMS-1710379, DMS-1509652
National Science Foundation Arctic Social Science Program

Keywords

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

ASJC Scopus subject areas

General Mathematics

Access to Document

10.2140/tunis.2020.2.567

Cite this

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