On the pathwidth of hyperbolic 3-manifolds
Abstract: According to Mostow's celebrated rigidity theorem, the geometry of closed hyperbolic 3-manifolds is already determined by their topology. In particular, the volume of such manifolds is a topological invariant and, as such, has been subject of investigations for half a century. Motivated by the algorithmic study of 3-manifolds, Maria and Purcell have recently shown that every closed hyperbolic 3-manifold M with volume vol(M) admits a triangulation with dual graph of treewidth at most C vol(M), for some universal constant C. Here we improve on this result by showing that the volume provides a linear upper bound even on the pathwidth of the dual graph of some triangulation, which can potentially be much larger than the treewidth. Our proof relies on a synthesis of tools from 3-manifold theory: generalized Heegaard splittings, amalgamations, and the thick-thin decomposition of hyperbolic 3-manifolds. We provide an illustrated exposition of this toolbox and also discuss the algorithmic .... https://www.cgt-journal.org/index.php/cgt/article/view/4
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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On the pathwidth of hyperbolic 3-manifolds ; volume:1 ; number:1 ; day:02 ; month:02 ; year:2022
Computing in Geometry and Topology ; 1, Heft 1 (02.02.2022)
- Creator
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Huszár, Kristóf
- DOI
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10.57717/cgt.v1i1.4
- URN
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urn:nbn:de:101:1-2022022417050683009429
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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15.08.2025, 7:34 AM CEST
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Associated
- Huszár, Kristóf
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Green Hyperbolic Complexes on Lorentzian Manifolds
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Intertwining operators for symmetric hyperbolic systems on globally hyperbolic manifolds
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Foundations of Hyperbolic Manifolds
The arithmetic of hyperbolic 3-manifolds
Torsion on hyperbolic manifolds of finite volume
Almost complex structures on hyperbolic manifolds
Twisted index on hyperbolic four-manifolds
Green Hyperbolic Complexes on Lorentzian Manifolds
Bootstrap bounds on closed hyperbolic manifolds
Lectures on the automorphism groups of Kobayashi hyperbolic manifolds
Intertwining operators for symmetric hyperbolic systems on globally hyperbolic manifolds