The fabrication of defined polymer objects of reduced dimensions such as polymer-coated nanoparticles (zero-dimensional (0D)), cylindrical brushes (1D), and polymer membranes (2D), is currently the subject of intense research. In particular, ultrathin polymer membranes with high aspect ratios are being discussed as novel materials for miniaturized sensors because they would provide extraordinary sensitivity and dynamic range when sufficient mechanical stability can be combined with flexibility and chemical functionality. Unlike current approaches that rely on crosslinking of polymer layers for stabilization, this report presents the preparation of a new class of polymer material, so-called "polymer carpets," a freestanding polymer brush grown by surface-initiated polymerization on a crosslinked 1-nm-thick monolayer. The solid-supported, as well as freestanding, polymer carpets are found to be mechanically robust and to react instantaneously and reversibly to external stimuli by buckling. The carpet mechanics and the dramatic changes of the film properties (optical, wetting) upon chemical stimuli are investigated in detail as they allow the development of completely new integrated micro-/nanotechnology devices.