当前位置: X-MOL 学术J. Topol. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
The top homology group of the genus 3 Torelli group
Journal of Topology ( IF 0.8 ) Pub Date : 2023-08-26 , DOI: 10.1112/topo.12308
Igor A. Spiridonov 1, 2
Affiliation  

The Torelli group of a genus g $g$ oriented surface Σ g $\Sigma _g$ is the subgroup I g $\mathcal {I}_g$ of the mapping class group Mod ( Σ g ) ${\rm Mod}(\Sigma _g)$ consisting of all mapping classes that act trivially on H 1 ( Σ g , Z ) ${\rm H}_1(\Sigma _g, \mathbb {Z})$ . The quotient group Mod ( Σ g ) / I g ${\rm Mod}(\Sigma _g) / \mathcal {I}_g$ is isomorphic to the symplectic group Sp ( 2 g , Z ) ${\rm Sp}(2g, \mathbb {Z})$ . The cohomological dimension of the group I g $\mathcal {I}_g$ equals to 3 g 5 $3g-5$ . The main goal of the present paper is to compute the top homology group of the Torelli group in the case g = 3 $g = 3$ as Sp ( 6 , Z ) ${\rm Sp}(6, \mathbb {Z})$ -module. We prove an isomorphism

中文翻译:

属 3 Torelli 群的顶级同源群

托雷利属组 G $g$ 定向表面 Σ G $\西格玛_g$ 是子群 G $\mathcal {I}_g$ 映射类组的 模组 Σ G ${\rm Mod}(\Sigma _g)$ 包含所有作用不大的映射类 H 1 Σ G , Z ${\rm H}_1(\Sigma _g, \mathbb {Z})$ 。商群 模组 Σ G / G ${\rm Mod}(\Sigma _g) / \mathcal {I}_g$ 与辛群同构 斯普 2 G , Z ${\rm Sp}(2g, \mathbb {Z})$ 。群的上同调维数 G $\mathcal {I}_g$ 等于 3 G - 5 $3g-5$ 。本文的主要目标是计算该情况下 Torelli 群的顶级同调群 G = 3 $g = 3$ 作为 斯普 6 , Z ${\rm Sp}(6, \mathbb {Z})$ -模块。我们证明同构
更新日期:2023-08-26
down
wechat
bug