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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJun 15th 2017
    • (edited Jun 15th 2017)

    I am looking for a decent account of the homotopy ring spectrum structure on KUKU with KU 0=BU×KU_0 = BU \times \mathbb{Z} that would be self-contained for a reader with good point-set topology background, but not involving E E_\infty or model category theory.

    What I find in the literature is all sketchy, but maybe I am looking in the wrong places.

    First, a discussion of the H-space structure on BU×BU\times \mathbb{Z} in the first place I find on p. 205 (213 of 251) in A Concise Course in Algebraic Topology. But for the crucial step it there only says:

    we merely affirm that, by fairly elaborate arguments, one can pass to colimits to obtain a product

    Is there a reference that would spell this out?

    Next, for the proof of the homotopy ring spectrum structure on KUKU, the idea is indicated on the first page of

    James McLure, H H_\infty-ring spectra via space-level homotopy theory (pdf)

    Is there a place where this would be spelled out in some detail?