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pro vyhledávání: '"Kawazumi, Nariya"'
Autor:
Kawazumi, Nariya
We introduce a natural cell decomposition of a closed oriented surface associated with a pants decomposition, and an explicit groupoid cocycle on the cell decomposition which represents each point of the Teichm\"uller space $\mathcal{T}_g$. We call i
Externí odkaz:
http://arxiv.org/abs/2408.04937
Autor:
Kawazumi, Nariya, Soulié, Arthur
We study the stable cohomology groups of the mapping class groups of surfaces with twisted coefficients given by the $d^{th}$ exterior powers of the first rational homology of the unit tangent bundles of the surfaces $\tilde{H}_{\mathbb{Q}}$. These c
Externí odkaz:
http://arxiv.org/abs/2311.01791
Autor:
Kawazumi, Nariya, Soulié, Arthur
We compute the stable cohomology groups of the mapping class groups of compact orientable surfaces with one boundary, with twisted coefficients given by the homology of the unit tangent bundle of the surface. This stable twisted cohomology is not fre
Externí odkaz:
http://arxiv.org/abs/2211.02793
Autor:
Kawazumi, Nariya
We introduce a twisted version of the Kawazumi-Zhang invariant $a_g(C) = \varphi(C)$ of a compact Riemann surface $C$ of genus $g \geq 1$, and discuss how it is related to the first Mumford-Morita-Milller class $e_1 = \kappa_1$ on the moduli space of
Externí odkaz:
http://arxiv.org/abs/2210.00532
Autor:
Kawazumi, Nariya, Vespa, Christine
Publikováno v:
Algebr. Geom. Topol. 23 (2023) 3089-3128
We show that the stable cohomology of automorphism groups of free groups with coefficients obtained by applying Hom(-,-) to tensor powers of the abelianization, is equipped with the structure of a wheeled PROP H. We define another wheeled PROP E by E
Externí odkaz:
http://arxiv.org/abs/2105.14497
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Autor:
Kawazumi, Nariya
The Turaev cobracket, a loop operation introduced by V. Turaev, which measures self-intersection of a loop on a surface, is a modification of a path operation introduced earlier by Turaev himself, as well as a counterpart of the Goldman bracket. In t
Externí odkaz:
http://arxiv.org/abs/1904.06686
Let $\Sigma$ be a compact connected oriented 2-dimensional manifold with non-empty boundary. In our previous work, we have shown that the solution of generalized (higher genus) Kashiwara-Vergne equations for an automorphism $F \in {\rm Aut}(L)$ of a
Externí odkaz:
http://arxiv.org/abs/1812.01159
For a compact oriented surface $\Sigma$ of genus $g$ with $n+1$ boundary components, the space $\mathfrak{g}(\Sigma)$ spanned by free homotopy classes of loops in $\Sigma$ carries the structure of a Lie bialgebra equipped with a natural decreasing fi
Externí odkaz:
http://arxiv.org/abs/1804.09566
Publikováno v:
Advances in Mathematics, 326, 1-53 (2018)
In this paper, we describe a surprising link between the theory of the Goldman-Turaev Lie bialgebra on surfaces of genus zero and the Kashiwara-Vergne (KV) problem in Lie theory. Let $\Sigma$ be an oriented 2-dimensional manifold with non-empty bound
Externí odkaz:
http://arxiv.org/abs/1703.05813