Short geodesics in hyperbolic 3–manifolds
Copyright policy )Short geodesics in hyperbolic 3–manifolds
For each $g \ge 2$, we prove existence of a computable constant $��(g) > 0$ such that if $S$ is a strongly irreducible Heegaard surface of genus $g$ in a complete hyperbolic 3-manifold $M$ and $��$ is a simple geodesic of length less than $��(g)$ in $M$, then $��$ is isotopic into $S$.
12 pages, corrected Lemma 1
- University of Michigan–Ann Arbor United States
- University of Michigan–Flint United States
- University of California, Davis United States
- University of Michigan Ann Arbor United States
Geometric Topology (math.GT), Geodesics in global differential geometry, 57M50, Mathematics - Geometric Topology, hyperbolic $3$–manifold, General geometric structures on low-dimensional manifolds, FOS: Mathematics, Knots and links in the \(3\)-sphere, Heegaard surface, geodesic, Heegaard decomposition, hyperbolic 3-manifold
Geometric Topology (math.GT), Geodesics in global differential geometry, 57M50, Mathematics - Geometric Topology, hyperbolic $3$–manifold, General geometric structures on low-dimensional manifolds, FOS: Mathematics, Knots and links in the \(3\)-sphere, Heegaard surface, geodesic, Heegaard decomposition, hyperbolic 3-manifold
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