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
References
Publication
Received: 15 May 2013
Accepted: 9 September 2013
Published: 31 January 2014
Authors
Vincent Emery
Department of Mathematics
Stanford University
Stanford, CA 94305
USA