Systoles and Dehn surgery for hyperbolic 3–manifolds

Lakeland, Grant S¹ ; Leininger, Christopher J¹

¹Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W Green St, 273 Altgeld Hall, Urbana, IL 61801, USA

Algebraic and Geometric Topology, Tome 14 (2014) no. 3, pp. 1441-1460

Résumé

Given a closed hyperbolic 3–manifold M of volume V , and a link L ⊂ M such that the complement M ∖ L is hyperbolic, we establish a bound for the systole length of M ∖ L in terms of V . This extends a result of Adams and Reid, who showed that in the case that M is not hyperbolic, there is a universal bound of 7.35534… As part of the proof, we establish a bound for the systole length of a noncompact finite volume hyperbolic manifold which grows asymptotically like 4 3 logV .

Détail

DOI : 10.2140/agt.2014.14.1441

Classification : 57M50
Keywords: systole, Kleinian group, isometric sphere

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