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.
Free division rings of fractions of crossed products of groups with
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Establishes Strong Atiyah Conjecture for finite-index torsion-free subgroups of Out(G) when G is a surface group, free group or RAAG, implying discrete von Neumann dimensions and Zero Divisor Conjecture for the group algebras.
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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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Outer automorphism groups and the Atiyah Conjecture
Establishes Strong Atiyah Conjecture for finite-index torsion-free subgroups of Out(G) when G is a surface group, free group or RAAG, implying discrete von Neumann dimensions and Zero Divisor Conjecture for the group algebras.