Strictly commutative complex orientation theory

@article{Hopkins2016StrictlyCC,
  title={Strictly commutative complex orientation theory},
  author={Michael J. Hopkins and Tyler Lawson},
  journal={Mathematische Zeitschrift},
  year={2016},
  volume={290},
  pages={83-101}
}
For a multiplicative cohomology theory E, complex orientations are in bijective correspondence with multiplicative natural transformations to E from complex bordism cohomology MU. If E is represented by a spectrum with a highly structured multiplication, we give an iterative process for lifting an orientation $$MU \rightarrow E$$MU→E to a map respecting this extra structure, based on work of Arone–Lesh. The space of strictly commutative orientations is the limit of an inverse tower of spaces… Expand
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References

SHOWING 1-10 OF 39 REFERENCES
GENERALIZED GROUP CHARACTERS AND COMPLEX ORIENTED COHOMOLOGY THEORIES
Let BG be the classifying space of a finite group G. Given a multiplicative cohomology theory E ⁄ , the assignment G 7i! E ⁄ (BG) is a functor from groups to rings, endowed with induction (transfer)Expand
For complex orientations preserving power operations, p-typicality is atypical
Abstract We show, for primes p ⩽ 13 , that a number of well-known MU ( p ) -rings do not admit the structure of commutative MU ( p ) -algebras. These spectra have complex orientations that factorExpand
SOME PROPERTIES OF THE THOM SPECTRUM OVER LOOP SUSPENSION OF COMPLEX PROJECTIVE SPACE
This note provides a reference for some properties of the Thom spectrum M over ΩΣCP 1 . Some of this material is used in recent work of Kitchloo and Morava. We determine the M -cohomology of CP 1 andExpand
A SPECTRUM LEVEL RANK FILTRATION IN ALGEBRAIC K-THEORY
THIS PAPER introduces a new filtration of the algebraic K-theory spectrum KR of a ring R, and investigates the subquotients of this filtration. KR is constructed from the category $P( R) of finitelyExpand
Units of ring spectra and Thom spectra
We review and extend the theory of Thom spectra and the associated obstruction theory for orientations. We recall (from May, Quinn, and Ray) that a commutative ring spectrum A has a spectrum of unitsExpand
Homotopy Theory of A∞ Ring Spectra and Applications to MU-Modules
We give a definition of a derivation of an A ∞ ring spectrum and relate this notion to topological Hochschild cohomology. Strict multi-plicative structure is introduced into Postnikov towers andExpand
Strictly commutative realizations of diagrams over the Steenrod algebra and topological modular forms at the prime 2
Previous work constructed a generalized truncated Brown-Peterson spectrum of chromatic height 2 at the prime 2 as an E∞-ring spectrum, based on the study of elliptic curves with level-3 structure. WeExpand
Filtered spectra arising from permutative categories
Abstract Given a special Γ-category 𝒞 satisfying some mild hypotheses, we construct a sequence of spectra interpolating between the spectrum associated to 𝒞 and the Eilenberg-Mac Lane spectrum Hℤ.Expand
THE MORAVA K-THEORIES OF EILENBERG-MACLANE SPACES AND THE CONNER-FLOYD CONJECTURE
Introduction. Of the many generalized homology theories available, very few are computable in practice except for the simplest of spaces. Standard homology and K-theory are the only ones which can beExpand
The Picard group of topological modular forms via descent theory
This paper starts with an exposition of descent-theoretic techniques in the study of Picard groups of $\mathbf{E}_{\infty}$-ring spectra, which naturally lead to the study of Picard spectra. We thenExpand
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