H∞ Ring Spectra and their Applications

Bruner, Robert R.; May, J. P.; McClure, James E.; Steinberger, Mark

doi:10.1007/bfb0075405

Cited by 205 publications

(259 citation statements)

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“…It is not hard to check that this is the same as the more classical definition given in [7] and thus to deduce the properties listed at the beginning of Section 5.…”

Section: Power Operationsmentioning

confidence: 77%

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Products on 𝑀𝑈-modules

Strickland

1999

Trans. Amer. Math. Soc.

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Abstract. Elmendorf, Kriz, Mandell and May have used their technology of modules over highly structured ring spectra to give new constructions of MUmodules 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[ ] * 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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“…It is not hard to check that this is the same as the more classical definition given in [7] and thus to deduce the properties listed at the beginning of Section 5.…”

Section: Power Operationsmentioning

confidence: 77%

“…which is natural for spaces X and strictly commutative ring spectra R. A good reference for such operations is [7]; in the case of M U , the earliest source is probably [28].…”

Section: Formal Group Theorymentioning

confidence: 99%

Products on 𝑀𝑈-modules

Strickland

1999

Trans. Amer. Math. Soc.

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“…We now briefly recall the Dyer-Lashof operations [2]. Let R be a commutative symmetric ring spectrum, H = HF p be a commutative symmetric ring spectrum modeling the mod-p Eilenberg-MacLane spectrum, and T = H ∧ R (although T can in general be any commutative H-algebra).…”

Section: This Is Natural In Based Spaces K and L And Is An Isomorphismentioning

confidence: 99%

“…The mod-2 homology H * (Sp(H); F 2 ) is the dual Steenrod algebra A * , whose DyerLashof structure is elaborated upon in [2] and can be deduced from the Nishida relations. In particular, one can show, by applying the operation (Sq m+1 ) * dual to Sq m+1 , that the generator ξ 1 of the dual Steenrod algebra in degree 1 supports nonzero Dyer-Lashof operations Q m for all m 1.…”

Section: This Is Natural In Based Spaces K and L And Is An Isomorphismentioning

confidence: 99%