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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A tower of spectra that realizes a chain complex


Author: Pedro A. Suárez
Journal: Proc. Amer. Math. Soc. 91 (1984), 133-138
MSC: Primary 55S10; Secondary 55S45
DOI: https://doi.org/10.1090/S0002-9939-1984-0735579-4
MathSciNet review: 735579
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Abstract: This paper presents the construction of a tower of spectra $ {Y_j}$ with $ k$-invariants coming from the relations $ {\text{S}}{{\text{q}}^1}(X{\text{S}}{{\text{q}}^{{2^{j + 1}}}}){\text{S}}{{\text{q}}^1}(X{\text{S}}{{\text{q}}^{{2^j}}}) = 0$ in $ A / A{\text{S}}{{\text{q}}^1}$, for $ 0 \leqslant j \leqslant 5$ and $ A$ = Steenrod algebra $ \mod 2$, such that $ {Y_5}$ has prescribed homotopy groups: $ {\pi _n}({Y_5}) = Z$ (integers) if $ n = {2^{j + 1}} - 2$, and zero otherwise.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0735579-4
Keywords: Tower of spectra, chain complex, Steenrod algebra, fibrations of spectra, cohomology exact sequences
Article copyright: © Copyright 1984 American Mathematical Society