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Prop of ribbon hypergraphs and strongly homotopy involutive Lie bialgebras
International Mathematics Research Notices. 2023. No. 7. P. 5685–5727.
Merkulov S., Khoroshkin A., Willwacher T., Letters in Mathematical Physics 2016 Vol. 106 P. 1199–1215
Motivated by the universal obstruction to the deformation quantization of Poisson structures in infinite dimensions we introduce the notion of quantizable odd Lie bialgebra. The main result of the paper is a construction of a highly non-trivial minimal resolution of the properad governing such Lie bialgebras, and its link with the theory of so called ...
Added: September 30, 2026
Merkulov S., Letters in Mathematical Physics 2016 Vol. 106 No. 2 P. 169–195
Using theory of props we prove a formality theorem associated with universal quantizations of (strongly homotopy) Lie bialgebras. ...
Added: September 30, 2026
Merkulov S., Willwacher T., Communications in Mathematical Physics 2018 Vol. 364 P. 505–578
We develop a new approach to deformation quantizations of Lie bialgebras and Poisson structures which goes in two steps. In the first step one associates to any Poisson (resp. Lie bialgebra) structure a so called quantizable Poisson (resp. Lie bialgebra) structure. We show explicit transcendental formulae for this correspondence. In the second step one deformation ...
Added: September 30, 2026
Merkulov S., Willwacher T., Compositio Mathematica 2020 Vol. 156 P. 2111–2148
We settle several fundamental questions about the theory of universal deformation quantization of Lie bialgebras by giving their complete classification up to homotopy equivalence. Moreover, we settle these questions in a greater generality: we give a complete classification of the associated universal formality maps. An important new technical ingredient introduced in this paper is a ...
Added: September 30, 2026
Merkulov S., Letters in Mathematical Physics 2023 Vol. 113 No. 3 Article 62
Added: December 19, 2025
Merkulov S., Živković M., Letters in Mathematical Physics 2022 Vol. 112 No. 13
We prove that the action of the Grothendieck–Teichmüller group on the genus completed properad of (homotopy) Lie bialgebras commutes with the reversing directions involution of the latter. We also prove that every universal quantization of Lie bialgebras is homotopy equivalent to the one which commutes with the duality involution exchanging Lie bracket and Lie cobracket. ...
Added: December 19, 2025
Springer, 2024.
This book explores toric topology, polyhedral products and related mathematics from a wide range of perspectives, collectively giving an overview of the potential of the areas while contributing original research to drive the subject forward in interesting new directions. Contributions to this volume were written in connection to the thematic program Toric Topology and Polyhedral Products held ...
Added: January 15, 2025
Pavutnitskiy F., Wu J., Algebraic and Geometric Topology 2019 Vol. 19 No. 1 P. 77–108
We use combinatorial group theory methods to extend the definition of the classical James–Hopf invariant to a simplicial group setting. This allows us to realize certain coalgebra idempotents at an sSet∗ level and obtain a functorial decomposition of the spectral sequence, associated with the lower p–central series filtration on a free simplicial group. ...
Added: October 29, 2020
Khoroshkin A., Mekulov S., Willwacher T., Letters in Mathematical Physics 2016 Vol. 106 No. 9 P. 1199–1215
Motivated by the obstruction to the deformation quantization of Poisson structures in infinitedimensions, we introduce the notion of a quantizable odd Lie bialgebra. The main result of the paper is a construction of the highly non-trivial minimal resolution of the properad governing such Lie bialgebras, and its link with the theory of so-called quantizable Poisson structures. ...
Added: September 11, 2016