Free-by-cyclic groups with coarse medians are algebraically characterized by unbranched blocks in maximal virtually F_n x Z subgroups and excessive linearity of completely split relative train track maps.
Measure equivalence rigidity of
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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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Characterizing hierarchically hyperbolic free by cyclic groups
Free-by-cyclic groups with coarse medians are algebraically characterized by unbranched blocks in maximal virtually F_n x Z subgroups and excessive linearity of completely split relative train track maps.
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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.