On the equivalence of the definitions of volume of representations

2014/04/15 by Kim, Sungwoon
#53C24 #53C35 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1404.3822

Abstract

Let G be a rank 1 simple Lie group and M be a connected orientable aspherical tame manifold. Assume that each end of M has amenable fundamental group. There are several definitions of volume of representations of the fundamental group of M into G. We give a new definition of volume of representations and furthermore, show that all definitions so far are equivalent.

Related

• Volume of representations and mapping degree
• Volume of representation varieties
• Integrality of Volumes of Representations
• Hyperbolic volume of representations of fundamental groups of cusped 3-manifolds
• Topological volumes of certain complete affine manifolds