On the formality of the little disks operad in positive characteristic

Brito, Pedro Boavida de; Horel, Geoffroy

doi:10.1112/jlms.12442

Cited by 6 publications

(13 citation statements)

References 35 publications

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“…The proof of Theorem B stands on the relation between the Goodwillie-Weiss tower and the little disks operad [Sin06, Tur14, DH12, BW18a], and the existence of Galois symmetries on the little disks operad that we established in [BH21]. Our main message in this paper is that by combining these two observations one obtains an interesting Galois action on the Goodwillie-Weiss tower.…”

Section: Galois Symmetries Of Knot Spacesmentioning

confidence: 78%

“…It is important to view E d as an ∞-operad since the p-completion functor L p does not preserve strict products, so applying p-completion aritywise to an operad does not directly produce an operad, but rather an ∞-operad. For more details, see [BH21].…”

Section: Galois Symmetries Of Knot Spacesmentioning

confidence: 99%

“…all its F p -homology groups are finite-dimensional) the p-completion L p (X) coincides with the homotopy limit of the pro-object X ∧ . This homotopy limit is denoted RMat in [BH21] and is the homotopy right adjoint of the pro-p-completion functor.…”

Section: Galois Symmetries Of Knot Spacesmentioning

confidence: 99%

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Galois symmetries of knot spaces

Brito¹,

Horel

2021

Compositio Math.

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We exploit the Galois symmetries of the little disks operads to show that many differentials in the Goodwillie–Weiss spectral sequences approximating the homology and homotopy of knot spaces vanish at a prime $p$ . Combined with recent results on the relationship between embedding calculus and finite-type theory, we deduce that the $(n+1)$ th Goodwillie–Weiss approximation is a $p$ -local universal Vassiliev invariant of degree $\leq n$ for every $n \leq p + 1$ .

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Section: Galois Symmetries Of Knot Spacesmentioning

confidence: 78%

Section: Galois Symmetries Of Knot Spacesmentioning

confidence: 99%

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Galois symmetries of knot spaces

Brito¹,

Horel

2021

Compositio Math.

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“…-We can first replace X by its p-completion which we will do implicitly from now on. In [4], an action of GT p , the p-complete Grothendieck-Teichmüller group is constructed on X. As a consequence of this action, it is shown in [4, Proposition 8.2] that for any unit α in Z p , there exists an automorphism α of X that acts by multiplication by α in homological degree (d − 1).…”

Section: Coformality Of Configuration Spacesmentioning

confidence: 99%

Homotopy transfer and formality

Drummond-Cole¹,

Horel²

2022

Annales De l'Institut Fourier

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In this paper, we prove that, given appropriate hypotheses, nformality of a differential graded algebraic structure is equivalent to the existence of a chain-level automorphism lifting a degree twisting isomorphism relative to a unit of order greater than n. A similar result with slightly different hypothesis was proved by Joana Cirici and the second author. We use the homotopy transfer theorem and an explicit inductive procedure in order to kill the higher operations. As an application of our result, we prove formality with coefficients in the p-adic integers of certain dg-algebras coming from hyperplane and toric arrangements and configuration spaces.Résumé. -Dans cet article nous montrons que, sous certaines hypothèses, la n-formalité d'une structure algébrique différentielle graduée est équivalente à l'existence d'un automorphisme au niveau des chaînes relevant un isomorphisme gradué tordant relatif à une unité d'ordre plus grand que n. Un résultat similaire sous des hypothèse légèrement différentes avait été prouvé par Joana Cirici et le second auteur. Nous utilisons le théorème de transfert homotopique et une procédure récursive explicite pour tuer les opérations supérieures. Comme application de ce résultat, nous prouvons la formalité à coefficients dans les entiers p-adiques de certaines dg-algèbres venant d'arrangements d'hyperplans ou d'arrangements toriques ainsi que des espaces de configurations.

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“…We can first replace X by its p-completion which we will do implicitly from now on. In [BdBH19], an action of GT p , the p-complete Grothendieck-Teichmüller group is constructed on X. As a consequence of this action, it is shown in [BdBH19, Proposition 8.2] that for any unit α in Z p , there exists an automorphism α ♯ of X that acts by multiplication by α in homological degree (d − 1).…”

Section: Applicationsmentioning

confidence: 99%

Homotopy transfer and formality

Drummond-Cole¹,

Horel²

2019

Preprint

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In [CH17,CH18], the second author and Joana Cirici proved a theorem that says that given appropriate hypotheses, n-formality of a differential graded algebraic structure is equivalent to the existence of a chain-level lift of a homology-level degree twisting automorphism using a unit of multiplicative order at least n.Here we give another proof of this result of independent interest and under slightly different hypotheses. We use the homotopy transfer theorem and an explicit inductive procedure in order to kill the higher operations. As an application of our result, we prove formality with coefficients in the p-adic integers of certain dg-algebras coming from hyperplane and toric arrangements and configuration spaces.

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On the formality of the little disks operad in positive characteristic

Cited by 6 publications

References 35 publications

Galois symmetries of knot spaces

Galois symmetries of knot spaces

Homotopy transfer and formality

Homotopy transfer and formality

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