A diameter bound for closed, hyperbolic 3-manifolds
Matthew E. White
TL;DR
This paper establishes an upper bound on the diameter of closed hyperbolic 3-manifolds based on the length of presentations of their fundamental groups, linking geometric and algebraic properties.
Contribution
It introduces a novel bound connecting the diameter of hyperbolic 3-manifolds with the algebraic complexity of their fundamental groups.
Findings
Diameter is bounded by presentation length
Links algebraic and geometric properties of manifolds
Provides a new tool for studying hyperbolic 3-manifolds
Abstract
We show there is an upper bound on the diameter of a closed, hyperbolic 3-manifold in terms of the length of any presentation of its fundamental group.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals