Equivariant Poincaré series and topology of valuations

Abstract

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 Poincar ́e series determines the equivariant topology of the collection of valuations.