On compact hyperbolic manifolds of Euler characteristic two
Geometric Topology
2014-10-01 v2
Abstract
We prove that for n>4 there is no compact arithmetic hyperbolic n-manifold whose Euler characteristic has absolute value equal to 2. In particular, this shows the nonexistence of arithmetically defined hyperbolic rational homology n-sphere with n even different than 4.
Cite
@article{arxiv.1304.3509,
title = {On compact hyperbolic manifolds of Euler characteristic two},
author = {Vincent Emery},
journal= {arXiv preprint arXiv:1304.3509},
year = {2014}
}
Comments
8 pages. v2: minor mistake at the end of the proof corrected. To appear in Alg. Geom. Topol