Algebraic & Geometric Topology 11 (2011) 1455–1469

DOI: 10.2140/agt.2011.11.1455

Abstract

We show that for every n ≥ 2 and any ϵ > 0 there exists a compact hyperbolic n–manifold with a closed geodesic of length less than ϵ. When ϵ is sufficiently small these manifolds are non-arithmetic, and they are obtained by a generalised inbreeding construction which was first suggested by Agol for n = 4. We also show that for n ≥ 3 the volumes of these manifolds grow at least as 1 ∕ ϵⁿ⁻² when ϵ → 0.

Keywords

systole, hyperbolic manifold, nonarithmetic lattice

Mathematical Subject Classification

Primary: 22E40, 53C22

References

Publication

Received: 4 October 2010
Revised: 24 January 2011
Accepted: 12 February 2011
Published: 17 May 2011

Authors