论文标题
绘制表面类的跨度同态和低维表示
Crossed homomorphisms and low dimensional representations of mapping class groups of surfaces
论文作者
论文摘要
我们继续研究由Franks-Handel和Korkmaz发起的映射类表面的映射组的低维线性表示。我们考虑$（2G+1）$ - 纯映射类的纯度映射类别的二维复杂线性表示，可将属于$ g $的紧凑定位表面。我们将$ g \ geq 7 $的此类表示形式进行了完整的分类，以与某些扭曲的$ 1 $ $ $ $ - $ 1 $ - 映射课程组的物种学组。一种新的成分是使用莫里塔（Morita）对相关扭曲的$ 1 $生物学组的计算。分类结果特别意味着$ g \ geq 7 $的尺寸$ 2G+1 $的不可约线表示，这标志着与情况的对比$ g = 2 $。
We continue the study of low dimensional linear representations of mapping class groups of surfaces initiated by Franks--Handel and Korkmaz. We consider $(2g+1)$-dimensional complex linear representations of the pure mapping class groups of compact orientable surfaces of genus $g$. We give a complete classification of such representations for $g \geq 7$ up to conjugation, in terms of certain twisted $1$-cohomology groups of the mapping class groups. A new ingredient is to use the computation of a related twisted $1$-cohomology group by Morita. The classification result implies in particular that there are no irreducible linear representations of dimension $2g+1$ for $g \geq 7$, which marks a contrast with the case $g=2$.
