论文标题
在表面上的曲线和环捆的代数
Lie algebras of curves and loop-bundles on surfaces
论文作者
论文摘要
W. Goldman和V. Turaev在$ \ Mathbb z $-模块上定义了由定向表面的自由同型循环类别（即其基本组的共轭类别）生成的。我们基于M. Chas给出的组合方法来开发这种构造代替薄质同位素的概括。我们使用它来提供几何证明，证明了通过CHAS猜想的Goldman-Turaev支架对简单曲线的表征。
W. Goldman and V. Turaev defined a Lie bialgebra structure on the $\mathbb Z$-module generated by free homotopy classes of loops of an oriented surface (i.e. the conjugacy classes of its fundamental group). We develop a generalization of this construction replacing homotopies by thin homotopies, based on the combinatorial approach given by M. Chas. We use it to give a geometric proof of a characterization of simple curves in terms of the Goldman-Turaev bracket, which was conjectured by Chas.
