Chain flaring and $L^{2}$-torsion of free-by-cyclic groups

Abstract

We introduce a condition on the monodromy of a free-by-cyclic group, $G_\phi$, called the chain flare condition, that implies that the $L^2$-torsion, $\rho^{(2)}(G_\phi)$, is non-zero. We conjecture that this condition holds whenever the monodromy is exponentially growing.