The invention relates to a branched or crosslinked anionic polyelectrolyte of at least one monomer having a partially- or totally-salified strong acid function, with at least one neutral monomer and at least one monomer having formula (I), wherein: R represents a linear or branched alkyl radical comprising between 8 and twenty carbon atoms, and n represents a number greater than or equal to 1 and less than or equal to twenty. The invention also relates to the use thereof as a thickener in topical compositions.