Simple closed geodesics in cusped hyperbolic 3-manifolds
Feihuang Xia
TL;DR
This paper proves that cusped finite-volume hyperbolic 3-manifolds contain infinitely many simple closed geodesics, expanding understanding of their geometric structure.
Contribution
It establishes the existence of infinitely many simple closed geodesics in cusped hyperbolic 3-manifolds, a significant advancement in geometric topology.
Findings
Existence of infinitely many simple closed geodesics
Application to cusped hyperbolic 3-manifolds
Enhancement of geometric understanding
Abstract
We show that cusped finite-volume hyperbolic 3-manifolds contain infinitely many simple closed geodesics.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Algebraic Geometry and Number Theory