Integrality of Volumes of Representations
Abstract
Let M be an oriented complete hyperbolic n-manifold of finite volume. Using the definition of volume of a representation previously given by the authors in [BucherBurgerIozzi2013] we show that the volume of a representation of the fundamental group of M into the connected component of the isometry group of hyperbolic n-space, properly normalized, takes integer values if n=2m is at least 4. If M is not compact and 3-dimensional, it is known that the volume is not locally constant. In this case we give explicit examples of representations with volume as arbitrary as the volume of hyperbolic manifolds obtained from M via Dehn fillings.
Keywords
Cite
@article{arxiv.1407.0562,
title = {Integrality of Volumes of Representations},
author = {Michelle Bucher and Marc Burger and Alessandra Iozzi},
journal= {arXiv preprint arXiv:1407.0562},
year = {2020}
}
Comments
According to the suggestions of the referee, the article has been almost completely rewritten with the respect to the first version