English

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

R2 v1 2026-06-21T23:58:26.895Z