Systoles of hyperbolic 4-manifolds
Ian Agol
TL;DR
This paper proves that in hyperbolic 4-manifolds, it is possible to find closed geodesics of arbitrarily small length, demonstrating the manifolds' geometric flexibility.
Contribution
The authors establish the existence of hyperbolic 4-manifolds with arbitrarily short closed geodesics, advancing understanding of their geometric properties.
Findings
Existence of hyperbolic 4-manifolds with arbitrarily small geodesics
Construction methods for such manifolds
Implications for hyperbolic geometry and topology
Abstract
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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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Computational Geometry and Mesh Generation