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# Steenrod and Dyer-Lashof Operations on $BU$

Timothy Lance
Transactions of the American Mathematical Society
Vol. 276, No. 2 (Apr., 1983), pp. 497-510
DOI: 10.2307/1999063
Stable URL: http://www.jstor.org/stable/1999063
Page Count: 14
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## 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 $H^\ast(BU, Z_{(p)})$ and $H_\ast(BU, Z_{(p)})$ 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) $BU \rightarrow BU$, and applications to the classifying spaces of surgery which arise in this fashion will appear shortly.

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