Summary: The equivariant with respect to a finite group action Poincaré series of a collection of $r$ valuations was defined earlier as a power series in $r$ variables with the coefficients from a modification of the Burnside ring of the group. Here we show that (modulo simple exceptions) the equivariant Poincaré series determines the equivariant topology of the collection of valuations.

14B05, 13A18, 14R20, 16W70

finite group actions, Poincaré series, plane valuations, equivariant topology