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Systoles of hyperbolic 4-manifolds

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arxiv math/0612290 v1 pith:VGQWZ65U submitted 2006-12-11 math.GT

Ian Agol This is my paper · ORCID
classification math.GT
keywords closedhyperbolicexistsgeodesiclengthmanifoldmanifoldsprove
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We prove that for any \e>0, there exists a closed hyperbolic 4-manifold with a closed geodesic of length < \e.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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  4. Systole, inradius and rigidity of cusped hyperbolic 3-manifolds

    math.GT 2026-06 unverdicted novelty 6.0 of 10

    Optimal systole-volume and inradius-volume inequalities are proved for cusped and closed hyperbolic 3-manifolds, with the figure-eight knot complement, its sister, the Gieseking manifold, and others as extremals.

  5. On Systole, Kissing Number and Volume of Arithmetic Manifolds

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    Expository introduction to arithmetic manifolds that details answers for systole and kissing number questions in 2D hyperbolic manifolds while summarizing higher-dimensional cases and posing open questions.

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