Under the Strong Atiyah Conjecture and vanishing b1^(2), L2-Betti numbers of character kernels define a polytope-induced Thurston seminorm on H^1(G;R), with combinatorial splitting-complexity interpretations for free-by-cyclic and admissible 3-manifold groups.
and Friedl, Stefan and Jackson, Nicholas , TITLE =
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Reshetikhin-Turaev knot polynomials are fixed-parameter tractable in the treewidth of the input diagram via tensor network contraction, yielding e^{O(sqrt n)} time.
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Thurston norm, polytopes and splitting complexity
Under the Strong Atiyah Conjecture and vanishing b1^(2), L2-Betti numbers of character kernels define a polytope-induced Thurston seminorm on H^1(G;R), with combinatorial splitting-complexity interpretations for free-by-cyclic and admissible 3-manifold groups.
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Fixed-parameter tractable computation of Reshetikhin--Turaev knot polynomials via tensor networks
Reshetikhin-Turaev knot polynomials are fixed-parameter tractable in the treewidth of the input diagram via tensor network contraction, yielding e^{O(sqrt n)} time.