Character varieties as a tensor product

JOURNAL OF ALGEBRA

卷:500

Article; Proceedings Paper

关键词: Character varieties;    Tensor products;    Hopf algebras;   

DOI  :  10.1016/j.jalgebra.2017.09.004

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free