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A NOTE ON A-ANNIHILATED GENERATORS OF H*QX

Part of: Homotopy theory Operations and obstructions

Published online by Cambridge University Press:  21 March 2019

HADI ZARE
HADI ZARE*
Affiliation:
Department of Mathematics School of Mathematics, Statistics, and Computer Science College of Science, University of TehranTehran14174, Iran e-mail: [email protected]
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Abstract

For a path connected space X, the homology algebra $H_*(QX; \mathbb{Z}/2)$ is a polynomial algebra over certain generators QIx. We reinterpret a technical observation, of Curtis and Wellington, on the action of the Steenrod algebra A on the Λ algebra in our terms. We then introduce a partial order on each grading of H*QX which allows us to separate terms in a useful way when computing the action of dual Steenrod operations $Sq^i_*$ on $H_*(QX; \mathbb{Z}/2)$. We use these to completely characterise the A-annihilated generators of this polynomial algebra. We then propose a construction for sequences I so that QIx is A-annihilated. As an application, we offer some results on the form of potential spherical classes in H*QX upon some stability condition under homology suspension. Our computations provide new numerical conditions in the context of hit problem.

MSC classification

Primary: 55S10: Steenrod algebra
Secondary: 55S12: Dyer-Lashof operations 55P47: Infinite loop spaces
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 62 , Issue 2 , May 2020 , pp. 281 - 295
Copyright
Copyright © Glasgow Mathematical Journal Trust 2019

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