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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Products on $MU$-modules
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by N. P. Strickland PDF
Trans. Amer. Math. Soc. 351 (1999), 2569-2606 Request permission


Elmendorf, Kriz, Mandell and May have used their technology of modules over highly structured ring spectra to give new constructions of $MU$-modules such as $BP$, $K(n)$ and so on, which makes it much easier to analyse product structures on these spectra. Unfortunately, their construction only works in its simplest form for modules over $MU[\frac {1}{2}]_*$ that are concentrated in degrees divisible by $4$; this guarantees that various obstruction groups are trivial. We extend these results to the cases where $2=0$ or the homotopy groups are allowed to be nonzero in all even degrees; in this context the obstruction groups are nontrivial. We shall show that there are never any obstructions to associativity, and that the obstructions to commutativity are given by a certain power operation; this was inspired by parallel results of Mironov in Baas-Sullivan theory. We use formal group theory to derive various formulae for this power operation, and deduce a number of results about realising $2$-local $MU_*$-modules as $MU$-modules.
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Additional Information
  • N. P. Strickland
  • Affiliation: Trinity College, Cambridge CB2 1TQ, England
  • Address at time of publication: Department of Pure Mathematics, University of Sheffield, Sheffield S3 7RH, United Kingdom
  • Email:
  • Received by editor(s): January 9, 1997
  • Published electronically: March 1, 1999
  • © Copyright 1999 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 351 (1999), 2569-2606
  • MSC (1991): Primary 55T25
  • DOI:
  • MathSciNet review: 1641115