Steenrod and Dyer-Lashof operations on 𝐵𝑈

Lance, Timothy

doi:10.1090/S0002-9947-1983-0688957-X

Steenrod and Dyer-Lashof operations on $B\textbf {U}$
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Trans. Amer. Math. Soc. 276 (1983), 497-510 Request permission

Abstract:

This paper describes a simple, fast algorithm for the computation of Steenrod and Dyer-Lashof operations on $BU$. The calculations are carried out in $H^{\ast }(BU,{{\mathbf {Z}}_{(p)}})$ and ${H_{\ast }}(BU,{{\mathbf {Z}}_{(p)}})$ where $p$ local lifts are determined by the values on primitives and Cartan formulas. This algorithm also provides a description of Steenrod and Dyer-Lashof operations on the fiber of any $H$ map (or infinite loop map) $BU \to BU$, and applications to the classifying spaces of surgery which arise in this fashion will appear shortly.

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