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This article is cited in 1 scientific paper (total in 1 paper)
The Dyer–Lashof algebra and the Steenrod algebra for generalized homology and cohomology
V. A. Smirnov Moscow State Pedagogical University
Abstract:
An analogue $\mathbb R$ of the Dyer–Lashof algebra $R$ and an analogue $\mathbb A$ of the Steenrod algebra $A$ are defined for generalized homology and cohomology theories. It is shown that if there is an $E_\infty$-multiplicative structure on a spectrum $\mathbb H$, then on the corresponding generalized cohomology $\mathbb H^*(X)$ of a topological space $X$ there is an action $\mathbb A\otimes \mathbb H^*(X)\to \mathbb H^*(X)$ of the Steenrod algebra, while if the space $X$ is an $E_\infty$-space, then on the generalized homology $\mathbb H^*(X)$ there is an action $\mathbb R\otimes \mathbb H_*(X)\to \mathbb H_*(X)$ of the Dyer–Lashof algebra. These actions are computed for cobordism of topological spaces. A connection is established between the Steenrod operations and the Landweber–Novikov operations.
Received: 03.06.1999
Citation:
V. A. Smirnov, “The Dyer–Lashof algebra and the Steenrod algebra for generalized homology and cohomology”, Mat. Sb., 190:12 (1999), 93–128; Sb. Math., 190:12 (1999), 1807–1842
Linking options:
https://www.mathnet.ru/eng/sm444https://doi.org/10.1070/sm1999v190n12ABEH000444 https://www.mathnet.ru/eng/sm/v190/i12/p93
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Abstract page: | 328 | Russian version PDF: | 182 | English version PDF: | 10 | References: | 55 | First page: | 1 |
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