Engenera

Chadwick, Steven Greg; Mandell, Michael A.

doi:10.2140/gt.2015.19.3193

Cited by 8 publications

(4 citation statements)

References 26 publications

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“…Now we give an alternative proof and mild generalization of the description of

E_{n}

‐orientations of ring spectra due to Chadwick and Mandell, see [, Theorem 3.2]. While their argument uses the general Thom isomorphism, we deduce this result directly from the universal property of Thom ring spectra.…”

Section: The Universal Multiplicative Property Of the Thom Spectrummentioning

confidence: 79%

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A simple universal property of Thom ring spectra

Camarena

Barthel

2018

Journal of Topology

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We give a simple universal property of the multiplicative structure on the Thom spectrum of an n‐fold loop map, obtained as a special case of a characterization of the algebra structure on the colimit of a lax scriptO‐monoidal functor. This allows us to relate Thom spectra to En‐algebras of a given characteristic in the sense of Szymik. As applications, we recover the Hopkins–Mahowald theorem realizing Hdouble-struckFp and HZ as Thom spectra, and compute the topological Hochschild homology and the cotangent complex of various Thom spectra.

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“…Now we give an alternative proof and mild generalization of the description of

E_{n}

Section: The Universal Multiplicative Property Of the Thom Spectrummentioning

confidence: 79%

“…We then show that any

n

‐fold loop map with Thom spectrum

M f

is canonically

E_{n - 1}

M f

‐orientable, thereby establishing a structured version of the Thom isomorphism. Moreover, we deduce a theorem of Chadwick and Mandell , describing

E_{n}

‐orientations.…”

Section: Introductionmentioning

confidence: 91%

A simple universal property of Thom ring spectra

Camarena

Barthel

2018

Journal of Topology

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“…Question Is there an

E_{4}

‐equivalence

{normalΣ}_{+}^{\infty} B U false[β^{- 1} false] ≃ M U P

? The authors find such an equivalence very believable, but find difficulties proving it that are related to the difficulties Chadwick and Mandell [9] encounter when trying to check whether the Quillen idempotent on

M U

E_{4}

.…”

Section: Introductionmentioning

confidence: 99%

“…Is there an E 4 -equivalence Σ ∞ + BU [β −1 ] MUP ? The authors find such an equivalence very believable, but find difficulties proving it that are related to the difficulties Chadwick and Mandell[9] encounter when trying to check whether the Quillen idempotent on MU is E 4 .Question 4. Is there an E ∞ -ring homomorphism MU −→ Σ ∞ be called periodic complex bordism, such as the Tate spectrum MU tS 1 .…”

mentioning

confidence: 99%

Exotic multiplications on periodic complex bordism

Hahn

Yuan

2020

Journal of Topology

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Victor Snaith gave a construction of periodic complex bordism by inverting the Bott element in the suspension spectrum of BU. This presents an E∞ structure on periodic complex bordism by different means than the usual Thom spectrum definition of the E∞-ring MUP. Here, we prove that these two E∞-rings are in fact different, though the underlying E2-rings are equivalent. Nonetheless, we prove that both rings E∞-orient KU ∧ 2 and other forms of K-theory.

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Real orientations of Lubin–Tate spectra

Hahn

Shi

2020

Invent. math.

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We show that Lubin-Tate spectra at the prime 2 are Real oriented and Real Landweber exact. The proof is by application of the Goerss-Hopkins-Miller theorem to algebras with involution. For each height n, we compute the entire homotopy fixed point spectral sequence for En with its C 2 -action given by the formal inverse. We study, as the height varies, the Hurewicz images of the stable homotopy groups of spheres in the homotopy of these C 2 -fixed points.

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E_ngenera

Abstract: Abstract. Let R be an E 2 ring spectrum with zero odd dimensional homotopy groups. Every map of ring spectra M U → R is represented by a map of E 2 ring spectra. If 2 is invertible in π 0 R, then every map of ring spectra M SO → R is represented by a map of E 2 ring spectra.

Cited by 8 publications

References 26 publications

A simple universal property of Thom ring spectra

A simple universal property of Thom ring spectra

Exotic multiplications on periodic complex bordism

Real orientations of Lubin–Tate spectra

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