The smallest Haken hyperbolic polyhedra
Christopher K. Atkinson, Shawn Rafalski
TL;DR
This paper identifies the hyperbolic Coxeter polyhedron with the smallest volume that contains an essential 2-suborbifold, providing a classification within hyperbolic 3-orbifolds based on their canonical decompositions.
Contribution
It determines the minimal volume hyperbolic Coxeter polyhedron with an essential 2-suborbifold, advancing understanding of hyperbolic 3-orbifold structures.
Findings
Identified the smallest volume hyperbolic Coxeter polyhedron with an essential 2-suborbifold.
Classified hyperbolic 3-orbifolds based on canonical decompositions.
Provided a comprehensive analysis of hyperbolic polyhedral 3-orbifolds.
Abstract
We determine the lowest volume hyperbolic Coxeter polyhedron whose corresponding hyperbolic polyhedral 3-orbifold contains an essential 2-suborbifold, up to a canonical decomposition along essential hyperbolic triangle 2-suborbifolds.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology