On compact hyperbolic manifolds of Euler characteristic two
classification
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keywords
hyperboliccharacteristiccompacteulerabsolutearithmeticarithmeticallydefined
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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-sphere with n even different than 4.
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