The sigma orientation is an H ∞ map

Ando, Matthew; Hopkins, Michael; Strickland, Neil P.

doi:10.1353/ajm.2004.0008

Cited by 62 publications

(113 citation statements)

References 21 publications

(39 reference statements)

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“…Strickland come to mind immediately, for example, and any interested reader would do well to look at [2], [3], [20], [21] [34], [38], and [39]. The table in section 2 of the paper by Hopkins and Gross [21] indicates just how far behind the times I am.…”

mentioning

confidence: 99%

(PRE-)Sheaves of Ring Spectra Over the Moduli Stack of Formal Group Laws

Goerss¹

2004

Axiomatic, Enriched and Motivic Homotopy Theory

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In the first part of this article, I will state a realization problem for diagrams of structured ring spectra, and in the second, I will discuss the moduli space which parametrizes the problem.While some of what I say is quite general, the ring spectra I have in mind will arise from the chromatic point of view, which uses the geometry of formal groups to organize stable homotopy theory. Thus, a subsidiary aim here is to reemphasize this connection between algebraic geometry and homotopy theory.

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mentioning

confidence: 99%

(PRE-)Sheaves of Ring Spectra Over the Moduli Stack of Formal Group Laws

Goerss¹

2004

Axiomatic, Enriched and Motivic Homotopy Theory

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“…These operations coincide with the ones constructed by Ando [And95], though the construction is not identical, since Ando did not have available to him the fact that the Morava E-theories are commutative S-algebras. Some discussion of these operations is given in [AHS04].…”

Section: Which Is a Homomorphism Into The Ring Of Grouplike Elements Inmentioning

confidence: 99%

The units of a ring spectrum and a logarithmic cohomology operation

Rezk

2006

J. Amer. Math. Soc.

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We construct a “logarithmic” cohomology operation on Morava E E -theory, which is a homomorphism defined on the multiplicative group of invertible elements in the ring E 0 ( K ) E^0(K) of a space K K . We obtain a formula for this map in terms of the action of Hecke operators on Morava E E -theory. Our formula is closely related to that for an Euler factor of the Hecke L L -function of an automorphic form.

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“…The E ∞ structures on these cobordism spectra derive from products and powers of manifolds, and work of Ando, Hopkins, Rezk, and Strickland (and their collaborators, among others) shows that refining maps out of cobordism spectra and related spectra to E ∞ (or H ∞ ) ring maps has implications in geometry as well as topology and stable homotopy theory (see, for example, [2,4,5]). An E ∞ ring structure brings with it many extra tools and much of the work of stable homotopy in the past two decades has involved producing E ∞ ring structures and E ∞ ring maps.…”

Section: Introductionmentioning

confidence: 99%