A linear, branched or cross-linked anionic polyelectrolyte, resulting from the polymerisation, for 100 molar percentage: a) 50% to 99% of monomeric units including a strong, free and partially or completely salified acid function ; b) 1% to 50% of a monomeric units of formula (I): CH2═CH(R1)-C(═O)—O—(CH2)n-CF3 (I), wherein R1 represents H or CH3, and n is 1, 2 or 3; c) optionally greater than 0% to 5% of monomeric units of formula (II): R2-C(═O)—O—[(CH2-CH(R4)-O]m-R3 (II), wherein m is 0 to 50, R2 represents an unsaturated aliphatic monovalent radical with 2 to 4 carbon atoms, R4 represents H, CH3 or CH3CH2 and R3 represents a linear or branched, saturated or unsaturated hydrocarbon aliphatic radical with 8 to 30 carbon atoms, and d) optionally greater than 0% to 5% of at least one monomer with diethylenic or polyethylenic cross-linking. The use thereof as a thickener in topical compositions.