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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Hybrid spaces with interesting cohomology

Author: Kathryn Lesh
Journal: Trans. Amer. Math. Soc. 347 (1995), 3247-3262
MSC: Primary 55S10; Secondary 55P15, 55P60
MathSciNet review: 1316857
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Abstract: Let $ p$ be an odd prime, and let $ R$ be a polynomial algebra over the Steenrod algebra with generators in dimensions prime to $ p$. To such an algebra is associated a $ p$-adic pseudoreflection group $ W$, and we assume that $ W$ is of order prime to $ p$ and irreducible. Adjoin to $ R$ a one-dimensional element $ z$, and give $ R[z]$ an action of the Steenrod algebra by $ \beta z = 0$ and $ \beta x = (\left\vert x \right\vert/2)zx$ for an even dimensional element $ x$. We show that the subalgebra of elements of $ R[z]$ consisting of elements of degree greater than one is realized uniquely, up to homotopy, as the cohomology of a $ p$-complete space. This space can be thought of as a cross between spaces studied by Aguade, Broto, and Notbohm, and the Clark-Ewing examples, further studied by Dwyer, Miller, and Wilkerson.

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Article copyright: © Copyright 1995 American Mathematical Society

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