arXiv subjects

Brian Paljug

Publications and source records attributed to Brian Paljug.

2 recordsLinked to original sources

arXiv2015

Tamarkin's construction is equivariant with respect to the action of the Grothendieck-Teichmueller group

Recall that Tamarkin's construction arXiv:math/9803025, arXiv:math/0003052 gives us a map from the set of Drinfeld associators to the set of homotopy classes of L-infinity quasi-isomorphisms for Hochschild cochains of a polynomial algebra. Due to results of V. Drinfeld (Algebra i Analiz 2, (1990)) and T. Willwacher arXiv:1009.1654 both the source and the target of this map are equipped with natural actions of the Grothendieck-Teichmueller group $GRT_1$. In this paper, we use the result from arXiv:1305.4699 to prove that this map from the set of Drinfeld associators to the set of homotopy classes of L-infinity quasi-isomorphisms for Hochschild cochains is $GRT_1$-equivariant.

math.KT↗

arXiv2015

Action of derived automorphisms on infinity-morphisms

In this paper we investigate how to simultaneously change homotopy algebras of a certain type and a corresponding infinity morphism between them, and show that this can be done in a homotopically unique way. More precisely, for a reduced cooperad C, given Ω(C)-algebras V and W and an infinity-morphism U from V to W, for any derivation ϕof Ω(C) we produce new Ω(C)-algebras V' and W' and a new infinity-morphism U' between them, that are unique up to homotopy. Operads play the central role in answering this question, in particular a 2-colored operad Cyl(C) that governs pairs of homotopy algebras and infinity-morphisms between them.

math.KT↗