For one-ended coherent right-angled Artin groups, splitting complexity along epimorphisms to Z equals the L2-Euler characteristic of the kernel, yielding a Thurston semi-norm via Friedl-Lück L2-polytopes.
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Several geometric and dynamical structures on 3-manifolds realize integral points on the boundary of the dual Thurston norm ball, with discussion of known results toward Thurston's Euler class conjecture.
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Thurston norm for coherent right-angled Artin groups via $L^2$-invariants
For one-ended coherent right-angled Artin groups, splitting complexity along epimorphisms to Z equals the L2-Euler characteristic of the kernel, yielding a Thurston semi-norm via Friedl-Lück L2-polytopes.
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Thurston norm and the Euler class
Several geometric and dynamical structures on 3-manifolds realize integral points on the boundary of the dual Thurston norm ball, with discussion of known results toward Thurston's Euler class conjecture.