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pro vyhledávání: '"MERKULOV, SERGEI"'
We prove that the Kontsevich graph complex $GC_d^{2}$ and its oriented version $OGC_{d+1}^2$ are quasi-isomorphic as dg Lie algebras.
Comment: 10 pages
Comment: 10 pages
Externí odkaz:
http://arxiv.org/abs/2411.19657
Autor:
Merkulov, Sergei
We study Maxim Kontsevich's graph complex $GC_d$ for any integer $d$ as well as its oriented and targeted versions, and show new short proofs of the theorems due to Thomas Willwacher and Marko Zivkovic which establish isomorphisms of their cohomology
Externí odkaz:
http://arxiv.org/abs/2311.06669
Autor:
Merkulov, Sergei
We study Thomas Willwacher's twisting endofunctor tw in the category of dg properads P under the operad of (strongly homotopy) Lie algebras. It is proven that if P is a properad under properad Lieb of Lie bialgebras , then the associated twisted prop
Externí odkaz:
http://arxiv.org/abs/2209.06742
Autor:
Merkulov, Sergei A.
The chain gravity properad introduced earlier by the author acts on the cyclic Hochschild of any cyclic $A_\infty$ algebra equipped with a scalar product of degree $-d$. In particular, it acts on the cyclic Hochschild complex of any Poincare duality
Externí odkaz:
http://arxiv.org/abs/2201.01122
Autor:
Merkulov, Sergei, Živković, Marko
We prove that the action of the Grothendieck-Teichm\"uller 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 bial
Externí odkaz:
http://arxiv.org/abs/2110.08792
Autor:
Khoroshkin, Anton, Merkulov, Sergei
We study the deformation complex of the dg wheeled properad of $\mathbb{Z}$-graded quadratic Poisson structures and prove that it is quasi-isomorphic to the even M. Kontsevich graph complex. As a first application we show that the Grothendieck-Teichm
Externí odkaz:
http://arxiv.org/abs/2109.07793
Autor:
Merkulov, Sergei A.
Let $\mathcal{M}_{g,n}$ be the moduli space of algebraic curves of genus $g$ with $m+n$ marked points decomposed into the disjoint union of two sets of cardinalities $m$ and $n$, and $H_c^{\bullet}(\mathcal{M}_{m+n})$ its compactly supported cohomolo
Externí odkaz:
http://arxiv.org/abs/2108.10644
Autor:
Merkulov, Sergei A.
Publikováno v:
In Journal of Pure and Applied Algebra October 2023 227(10)
Autor:
Andersson, Assar, Merkulov, Sergei
We study homotopy theory of the wheeled prop controlling Poisson structures on arbitrary formal graded finite-dimensional manifolds and prove, in particular, that Grothendieck-Teichmueller group acts on that wheeled prop faithfully and homotopy non-t
Externí odkaz:
http://arxiv.org/abs/1911.09089
Autor:
Merkulov, Sergei
Publikováno v:
AMS Proceedings of Symposia in Pure Mathematics, "Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry", vol. 103 (2021)
This paper attempts to provide a more or less self-contained introduction into theory of the Grothendieck-Teichmueller group and Drinfeld associators using the theory of operads and graph complexes.
Comment: One reference is added
Comment: One reference is added
Externí odkaz:
http://arxiv.org/abs/1904.13097