of a) 80% or more and monomer units derived from monomers containing a weak acid functional group of 99.5% or less of the mass ratio, b) 0.5% or more and 20% or less of the mass ratio, the formula (1a): R- (CH. 2. ). 3. -Si (CH. 3. ). 2. - [O-Si (CH 3 ). 2. -]. n. O-Si (CH. 3. ). 2. - (. CH 2 ). 3. -R (1a) (wherein, R is a monovalent radical :-( O-CH 2 -CH 2 -........) X [ .... O-CH 2 -CH (CH 3 ) -.] yO-C (= O) -CH = CH 2 monomer of the represent), or formula (Ib): Si (CH 3 ). 3. - [O-Si (CH 3 ). 2. -]. m. [O-Si (CH. 3. ) [(CH. 2. ). 3. -R] -]. p. O-Si (CH. 2. ). 3. Monomers (Ib), c) optionally, at least one formula of 0% ultra and 5% of the mass ratio (II): R. 2. -C (= O) -O -.. [........ (CH 2 -CH (R 4 ) -O] m . -R. 3. monomer unit derived from a monomer (II), d) optionally, at least one of 0% ultra and less than 5% of the mass ratio diethylene system or anionic polymer electrolyte obtained by polymerization of the polyethylene-based cross-linking monomers, methods of preparing them, and their use as thickeners in topical compositions.BACKGROUND.a)80%以上かつ99.5%以下の質量比の弱酸官能基を含むモノマーに由来するモノマー単位、b)0.5%以上かつ20%以下の質量比の、式(1a):R-(CH2)3-Si(CH3)2-[O-Si(CH3)2-]nO-Si(CH3)2-(CH2)3-R(1a)(式中、Rは一価ラジカル:-(O-CH2-CH2-)x[O-CH2-CH(CH3)-]yO-C(=O)-CH=CH2を表す)のモノマー、又は式(Ib):Si(CH3)3-[O-Si(CH3)2-]m[O-Si(CH3)[(CH2)3-R]-]pO-Si(CH2)3(Ib)のモノマー、c)任意で、0%超かつ5%以下の質量比の少なくとも1つの式(II):R2-C(=O)-O-[(CH2-CH(R4)-O]m-R3(II)のモノマーに由来するモノマー単位、d)任意で、0%超かつ5%以下の質量比の少なくとも1つのジエチレン系又はポリエチレン系架橋モノマーの重合によって得られるアニオン性高分子電解質、それを調製する方法、及び局所組成物の増粘剤としてのその使用。【選択図】なし