Dynamics on the SU(2,1)-character variety of the one-holed torus
arxiv(2024)
摘要
We study the relative SU(2,1)-character varieties of the one-holed torus, and
the action of the mapping class group on them. We use an explicit description
of the character variety of the free group of rank two in SU(2,1) in terms of
traces, which allow us to describe the topology of the character variety. We
then combine this description with a generalization of the Farey graph adapted
to this new combinatorial setting, using ideas introduced by Bowditch. Using
these tools, we can describe an open domain of discontinuity for the action of
the mapping class group which strictly contains the set of convex-cocompact
characters, and we give several characterizations of representations in this
domain.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要