Systoles of hyperbolic manifolds

Belolipetsky, Mikhail V¹ ; Thomson, Scott A²

¹Department of Mathematical Sciences, Durham University, South Road, Durham, DH1 3LE, United Kingdom, Institute of Mathematics, Koptyuga 4, 630090 Novosibirsk, Russia
²Department of Mathematical Sciences, Durham University, South Road, Durham, DH1 3LE, United Kingdom

Algebraic and Geometric Topology, Tome 11 (2011) no. 3, pp. 1455-1469

Résumé

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.

Détail

DOI : 10.2140/agt.2011.11.1455

Classification : 22E40, 53C22
Keywords: systole, hyperbolic manifold, nonarithmetic lattice

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