Mixed tête-à-tête twists as monodromies associated with holomorphic function germs

Abstract: T^ete-`a-t^ete graphs were introduced by N. A'Campo in 2010 with the goal of modeling the monodromy of isolated plane curves. Mixed t^ete-`a-t^ete graphs provide a generalization which define mixed t^ete-`a-t^ete twists, which are pseudo-periodic automorphisms on surfaces. We characterize the mixed t^ete-`a-t^ete twists as those pseudo-periodic automorphisms that have a power which is a product of right-handed Dehn twists around disjoint simple closed curves, including all boundary components. It follows that the class of t^ete-`a-t^ete twists coincides with that of monodromies associated with reduced function germs on isolated complex surface singularities.