Many cusped hyperbolic 3-manifolds do not bound geometrically
Geometric Topology
2020-03-19 v3 Combinatorics
Metric Geometry
Abstract
In this note, we show that there exist cusped hyperbolic -manifolds that embed geodesically, but cannot bound geometrically. Thus, being a geometric boundary is a non-trivial property for such manifolds. Our result complements the work by Long and Reid on geometric boundaries of compact hyperbolic -manifolds, and by Kolpakov, Reid and Slavich on embedding arithmetic hyperbolic manifolds.
Cite
@article{arxiv.1811.05509,
title = {Many cusped hyperbolic 3-manifolds do not bound geometrically},
author = {Alexander Kolpakov and Alan W. Reid and Stefano Riolo},
journal= {arXiv preprint arXiv:1811.05509},
year = {2020}
}
Comments
11 pages, 3 figures; to appear in Proceedings AMS