Hopf constructions and higher projective planes for iterated loop spaces

Authors:
Nicholas J. Kuhn, Michael Slack and Frank Williams

Journal:
Trans. Amer. Math. Soc. **347** (1995), 1201-1238

MSC:
Primary 55P35; Secondary 55P45, 55P47, 55S12

DOI:
https://doi.org/10.1090/S0002-9947-1995-1282890-9

MathSciNet review:
1282890

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Abstract: We define a category, (for each and ), of spaces with strong homotopy commutativity properties. These spaces have just enough structure to define the Dyer-Lashof operations for -fold loop spaces. The category is very convenient for applications since its objects and morphisms are defined in a homotopy invariant way. We then define a functor, , from to the homotopy category of spaces and show to be left adjoint to the -fold loop space functor. We then show how one can exploit this adjointness in cohomological calculations to yield new results about iterated loop spaces.

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DOI:
https://doi.org/10.1090/S0002-9947-1995-1282890-9

Article copyright:
© Copyright 1995
American Mathematical Society