A process prepares a cross-linked polymer containing urethane groups and silicon atoms. Starting materials of the process include a compound A) with a five-membered cyclic monothiocarbonate group, a compound B) with an amino group, selected from primary or secondary amino groups or blocked amino groups, and optionally, a compound C) with at least one functional group that reacts with a group —SH. One of the compounds contains a silicon-functional group. In one example of the process, compounds A) and B), and optionally C), are then reacted under exclusion of water to obtain a polymer with curable silicon-functional groups. The polymer is applied to a surface, gap, or a three-dimensional template. The silicon-functional groups are cured with ambient water. The polymer contains 0.001 to 0.3 mol of silicon per 100 g of the polymer.