Volume and structure of hyperbolic 3-manifolds
Teruhiko Soma
TL;DR
This paper extends Gromov-Thurston's principle to infinite volume hyperbolic 3-manifolds with finitely generated fundamental groups, providing a new proof of the Ending Lamination Theorem based on maximum volume laws.
Contribution
It generalizes the principle to a broader class of hyperbolic 3-manifolds and offers a novel proof of a major theorem using volume laws.
Findings
Gromov-Thurston's principle applies to infinite volume hyperbolic 3-manifolds
New proof of the Ending Lamination Theorem
Relies on maximum volume law for hyperbolic 3-simplices
Abstract
In this paper, we show that Gromov-Thurston's principle works for hyperbolic 3-manifolds of infinite volume and with finitely generated fundamental group. As an application, we have a new proof of Ending Lamination Theorem. Our proof essentially relays only on Maximum Volume Law for hyperbolic 3-simplices.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Geometric Analysis and Curvature Flows