Discrete representations of finitely generated groups into \rm PSL(2,ℝ)

2020/10/30 by Liang, Hao
#20F67 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Primary: 20F65 #Secondary: 30C20

paper · doi:10.48550/arxiv.2010.16008

Abstract

We prove a factorization theorem for Fuchsian groups similar to those proved by Agol and Liu for 3-manifold groups. As an application, we build Makanin-Razborov diagrams, which parametrize the collection of all discrete representations from an arbitrary but fixed finitely generated group G to \rm PSL(2, ℝ). We define a new class of groups called \rm PSL(2, ℝ)-discrete limit groups and then use the factorization theorem to obtain useful information about this class of groups.

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