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pro vyhledávání: '"Massuyeau, Gwenael"'
We consider the associated graded $\bigoplus_{k\geq 1} \Gamma_k \mathcal{I} / \Gamma_{k+1} \mathcal{I} $ of the lower central series $\mathcal{I} = \Gamma_1 \mathcal{I} \supset \Gamma_2 \mathcal{I} \supset \Gamma_3 \mathcal{I} \supset \cdots$ of the
Externí odkaz:
http://arxiv.org/abs/2407.07981
Autor:
Habiro, Kazuo, Massuyeau, Gwenael
The Johnson-Morita theory is an algebraic approach to the mapping class group of a surface, in which one considers its action on the successive nilpotent quotients of the fundamental group of the surface. In this paper, we develop an analogue of this
Externí odkaz:
http://arxiv.org/abs/2401.07705
Autor:
Massuyeau, Gwenael
Publikováno v:
Winter Braids Lecture Notes, Tome 8 (2021), Expos\'e no. 1, 41 pages
By classical results of Rochlin, Thom, Wallace and Lickorish, it is well-known that any two 3-manifolds (with diffeomorphic boundaries) are related one to the other by surgery operations. Yet, by restricting the type of the surgeries, one can define
Externí odkaz:
http://arxiv.org/abs/2301.12428
Autor:
Faes, Quentin, Massuyeau, Gwenael
The Johnson kernel is the subgroup of the mapping class group of a closed oriented surface that is generated by Dehn twists along separating simple closed curves. The rational abelianization of the Johnson kernel has been computed by Dimca, Hain and
Externí odkaz:
http://arxiv.org/abs/2209.12740
Autor:
Massuyeau, Gwenael, Moussard, Delphine
Publikováno v:
Canad. J. Math. 73:6 (2021) 1743-1770
We prove a "splicing formula" for the LMO invariant, which is the universal finite-type invariant of rational homology $3$-spheres. Specifically, if a rational homology $3$-sphere $M$ is obtained by gluing the exteriors of two framed knots $K_1 \subs
Externí odkaz:
http://arxiv.org/abs/2001.03358
Publikováno v:
Topology and Geometry: A Collection of Essays Dedicated to Vladimir G. Turaev, 357-398. Ed. A. Papadopoulos, Eur. Math. Soc., Berlin, 2021
The generalized Dehn twist along a closed curve in an oriented surface is an algebraic construction which involves intersections of loops in the surface. It is defined as an automorphism of the Malcev completion of the fundamental group of the surfac
Externí odkaz:
http://arxiv.org/abs/1909.09496
Autor:
Kuno, Yusuke, Massuyeau, Gwenael
Publikováno v:
Algebr. Geom. Topol. 21 (2021) 697-754
Let $\Sigma$ be a compact oriented surface. The Dehn twist along every simple closed curve $\gamma \subset \Sigma$ induces an automorphism of the fundamental group $\pi$ of $\Sigma$. There are two possible ways to generalize such automorphisms if the
Externí odkaz:
http://arxiv.org/abs/1902.02592
Autor:
Habiro, Kazuo, Massuyeau, Gwenael
Publikováno v:
J. Algebra 510 (2018) 205-258
The Johnson filtration of the mapping class group of a compact, oriented surface is the descending series consisting of the kernels of the actions on the nilpotent quotients of the fundamental group of the surface. Each term of the Johnson filtration
Externí odkaz:
http://arxiv.org/abs/1707.07428
Autor:
Habiro, Kazuo, Massuyeau, Gwenael
Publikováno v:
Quantum Topol. 12:4 (2021) 593-703
Using an extension of the Kontsevich integral to tangles in handlebodies similar to a construction given by Andersen, Mattes and Reshetikhin, we construct a functor $Z:\mathcal{B}\to \widehat{\mathbb{A}}$, where $\mathcal{B}$ is the category of botto
Externí odkaz:
http://arxiv.org/abs/1702.00830
Autor:
Massuyeau, Gwenael, Sakasai, Takuya
Publikováno v:
J. Topol. Anal. 12:3 (2020) 775-818
Morita introduced in 2008 a 1-cocycle on the group of homology cobordisms of surfaces with values in an infinite-dimensional vector space. His 1-cocycle contains all the "traces" of Johnson homomorphisms which he introduced fifteen years earlier in h
Externí odkaz:
http://arxiv.org/abs/1606.08244