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The Curtis–Wellington
spectral sequence through cohomology
Dana Hunter |
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Algebraic & Geometric Topology 25 (2025) 3315–3340
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Abstract |
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We study stable homotopy groups through unstable methods applied to their representing infinite loop space , as pioneered by Curtis and Wellington. Using cohomology instead of homology, we find a width filtration whose subquotients are simple quotients of Dickson algebras, which thus gives a new filtration of stable homotopy groups. We make initial calculations and determine towers in the resulting width spectral sequence. We also make calculations related to the image of , and prove that the homomorphism induces a splitting of the indecomposables of the cohomology of . |
Keywords
stable homotopy groups, infinite loop space, image of $J$
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Mathematical Subject Classification
Primary: 55Q40
Secondary: 55P47, 55Q50
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References |
Publication
Received: 12 October 2022
Revised: 14 June 2023
Accepted: 26 July 2023
Published: 1 October 2025
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Authors |
| Dana Hunter | ||
| Department of Mathematics University of Oregon Eugene, OR United States |
Department of Mathematics Kalamazoo College Kalamazoo, MI United States |
Mathematics Department Fort Lewis College Durango, CO United States |
| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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