#### Volume 14, issue 2 (2014)

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On compact hyperbolic manifolds of Euler characteristic two

### Vincent Emery

Algebraic & Geometric Topology 14 (2014) 853–861
##### 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 $n$–spheres with $n$ even and different than $4$.

 Dedicated to the memory of Colin Maclachlan
##### Keywords
locally symmetric spaces, hyperbolic manifolds, arithmetic groups, rational homology spheres
##### Mathematical Subject Classification 2010
Primary: 22E40
Secondary: 55C35, 51M25