论文标题
关于映射类组的符号表示的溢流性
On the surjectivity of the Symplectic representation of the mapping class group
论文作者
论文摘要
在本说明中，我们研究了映射类组的合成性表示。特别是，我们讨论了限于某些映射类别的表示形式的表现。众所周知，代表本身是汇总的。实际上，在限制了伪-Anosov映射类后，表示形式仍然是汇总的。但是，我们表明，即使在可定位的伪anosovs上表示表示，即使在将其代码分子降低到具有双佩隆领先的特征值的整数符号矩阵之后，溢流力也不会达到。为了证明非解释率，我们明确地构建了一个无限型矩阵的家族，其双帝国领先的特征值无法作为可定向的伪anosov映射类别的符号表示。
In this note, we study the symplectic representation of the mapping class group. In particular, we discuss the surjecivity of the representation restricted to certain mapping classes. It is well-known that the representation itself is surjective. In fact the representation is still surjective after restricting on pseudo-Anosov mapping classes. However, we show that the surjectivity does not hold when the representation is restricted on orientable pseudo-Anosovs, even after reducing its codomain to integer symplectic matrices with a bi-Perron leading eigenvalue. In order to prove the non-surjectivity, we explicitly construct an infinite family of symplectic matrices with a bi-Perron leading eigenvalue which cannot be obtained as the symplectic representation of an orientable pseudo-Anosov mapping class.
