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- W4287173690 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 investigated 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 consequences of the result." @default.
- W4287173690 created "2022-07-25" @default.
- W4287173690 creator A5062642592 @default.
- W4287173690 date "2022-02-02" @default.
- W4287173690 modified "2023-10-16" @default.
- W4287173690 title "On the pathwidth of hyperbolic 3-manifolds" @default.
- W4287173690 doi "https://doi.org/10.57717/cgt.v1i1.4" @default.
- W4287173690 hasPublicationYear "2022" @default.
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