Integrality of Volumes of Representations
Abstract
Let M be an oriented complete hyperbolic nmanifold 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 nspace, properly normalized, takes integer values if n=2m is at least 4. If M is not compact and 3dimensional, 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.
 Publication:

arXiv eprints
 Pub Date:
 July 2014
 arXiv:
 arXiv:1407.0562
 Bibcode:
 2014arXiv1407.0562B
 Keywords:

 Mathematics  Geometric Topology;
 53C24;
 22E40;
 22E41
 EPrint:
 According to the suggestions of the referee, the article has been almost completely rewritten with the respect to the first version