Norms that are sums of absolute values of rational linear functionals are exactly the nonvanishing Thurston norms of closed oriented graph manifolds, which can be chosen to fiber over the circle or not.
The efficient certification of knottedness and Thurston norm
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The Thurston norm of graph manifolds
Norms that are sums of absolute values of rational linear functionals are exactly the nonvanishing Thurston norms of closed oriented graph manifolds, which can be chosen to fiber over the circle or not.