AI 中文总结
本文给出曲面拼布分解及带色拼布分解变换群胚的表示，通过构造二维胞腔复形实现，还证明Torelli群在这类复形上自由作用。
AI 中文摘要
我们给出曲面的拼布分解变换群胚的一个表示，拼布分解是曲面的裤子分解并添加“接缝”。我们考虑曲面的带色拼布分解，其中拼布分解的一侧被着色。我们还给出曲面的带色拼布分解变换群胚的一个表示。这些群胚的表示通过构造连通且单连通的二维胞腔复形实现，其0-胞腔为曲面上的这类（合痕意义下）结构。在本文后半部分，我们证明Torelli群（更准确地说，是曲面映射类群的无挠子群）在这些复形上自由作用。
英文摘要
We give a presentation of a groupoid of transformations of quilt decompositions of a surface, which are pants decompositions of the surface with the addition of "seams". We consider colored quilt decompositions of a surface, where one side of a quilt decomposition is colored. We also give a presentation of a groupoid of transformations of colored quilt decompositions of a surface. These presentations of such groupoids are realized by constructing connected and simply-connected two-dimensional cell complexes whose 0-cell are these up-to-isotopy structures on the surface. In the latter part of this paper, we show that Torelli group (or more precisely, a torsion-free subgroup of a mapping class group of a surface) acts on these complexes freely.
Comments45 pages, 44 figures
