Character varieties as a tensor product
Character varieties as a tensor product
复制标题
作为张量积的字符品种
DOI：
10.1016/j.jalgebra.2017.09.004
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Sasha Patotski
中科院分区：
文献类型：
--
作者：
M. Kassabov;Sasha Patotski
在这个简短的说明中，我们表明，表示和字符品种的离散群可以被视为张量积的适当函子上的PROP的余交换Hopf代数。这种观点有几个有趣的应用。首先，它给出了一个直接的方法来推导函子发送一个离散群的功能在其表示簇，这导致表示同调。第二，使用适当的变形的函子参与这个建设，可以得到变形的表示和特征品种的基本群的3-流形，并可能导致更好地理解量子表示的映射类群。
In this short note we show that representation and character varieties of discrete groups can be viewed as tensor products of suitable functors over the PROP of cocommutative Hopf algebras. Such view point has several interesting applications. First, it gives a straightforward way of deriving the functor sending a discrete group to the functions on its representation variety, which leads to representation homology. Second, using a suitable deformation of the functors involved in this construction, one can obtain deformations of the representation and character varieties for the fundamental groups of 3-manifolds, and could lead to better understanding of quantum representations of mapping class groups.