Geodesic
On compact hyperbolic manifolds of Euler characteristic two
Emery, Vincent1
1Department of Mathematics, Stanford University, Stanford, CA 94305, USA
Algebraic and Geometric Topology, Tome 14 (2014) no. 2, pp. 853-861
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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.

DOI : 10.2140/agt.2014.14.853
Classification : 22E40, 55C35, 51M25
Keywords: locally symmetric spaces, hyperbolic manifolds, arithmetic groups, rational homology spheres

Emery, Vincent  1

1 Department of Mathematics, Stanford University, Stanford, CA 94305, USA 
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Emery, Vincent. On compact hyperbolic manifolds of Euler characteristic two. Algebraic and Geometric Topology, Tome 14 (2014) no. 2, pp. 853-861. doi: 10.2140/agt.2014.14.853

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