The invention relates to a polysaccharide polymer of formula (I):PS—(O—CO-L-X)a(OH)b (I)in which PS denotes the basic backbone of the polysaccharide bearing the hydroxyl groupsL is a divalent hydrocarbon-based group comprising from 1 to 20 carbon atomsX denotes a photoactive group of azide or diazirine typea denotes the content of OH groups substituted with the photoactive groupb denotes the content of unsubstituted free OH groupsa being between 0.02 and 0.5 b being between 0.5 and 0.98and a+b=1.The invention also relates to a composition comprising the polymer (I) in a physiologically acceptable medium, and also to a cosmetic process for caring for the skin, comprising the topical application to the skin of said composition and exposure of the treated skin to light radiation.
