On compact hyperbolic manifolds of Euler characteristic two

Emery, Vincent

doi:10.2140/agt.2014.14.853

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On compact hyperbolic manifolds of Euler characteristic two

Vincent Emery

Algebraic & Geometric Topology 14 (2014) 853–861

DOI: 10.2140/agt.2014.14.853

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

Volume 14, issue 2 (2014)