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Transactions of the American Mathematical Society

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

 

 

Steenrod and Dyer-Lashof operations on $ B{\bf U}$


Author: Timothy Lance
Journal: Trans. Amer. Math. Soc. 276 (1983), 497-510
MSC: Primary 55S10; Secondary 55R45, 55S12
MathSciNet review: 688957
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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,{{\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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DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0688957-X
Article copyright: © Copyright 1983 American Mathematical Society