论文标题
积极表示的参数化空间
Parametrizing spaces of positive representations
论文作者
论文摘要
使用Lusztig在分裂的真实谎言组V. Fock和A. Goncharov中的总阳性已引入了正（框架）表示空间。对于一般的半圣事群，O. Guichard和A. Wienhard最近引入了Lusztig的总积极性的概括。他们还引入了积极表示的相关空间。在这里，我们考虑了刺穿表面的基本组的阳性框架表示的相应空间。我们给出了框架积极表示空间的几个参数化。使用这些参数化，我们描述了它们的拓扑结构及其同型类型。我们表明，框架积极表示空间的连接组件数量与积极表示空间的连接组件的数量一致，并确定了简单谎言组的这个数字。一路上，我们还为任意的半神经谎言组（刺破表面的基本组的表示空间）进行参数化，该表面相对于表面的固定理想三角剖分横向。
Using Lusztig's total positivity in split real Lie groups V. Fock and A. Goncharov have introduced spaces of positive (framed) representations. For general semisimple Lie groups a generalization of Lusztig's total positivity was recently introduced by O. Guichard and A. Wienhard. They also introduced the associated space of positive representations. Here we consider the corresponding spaces of positive framed representations of the fundamental group of a punctured surface. We give several parametrizations of the spaces of framed positive representations. Using these parametrizations, we describe their topology and their homotopy type. We show that the number of connected components of the space of framed positive representations agrees with the number of connected components of the space of positive representations, and determine this number for simple Lie groups. Along the way, we also parametrize, for an arbitrary semisimple Lie group, the space of representations of the fundamental group of a punctured surface which are transverse with respect to a fixed ideal triangulation of the surface.
