  We study the indentation of a thin elastic film floating at the surface of a
liquid. We focus on the onset of radial wrinkles at a threshold indentation
depth and the evolution of the wrinkle pattern as indentation progresses far
beyond this threshold. Comparison between experiments on thin polymer films and
theoretical calculations shows that the system very quickly reaches the Far
from Threshold (FT) regime, in which wrinkles lead to the relaxation of
azimuthal compression. Furthermore, when the indentation depth is sufficiently
large that the wrinkles cover most of the film, we recognize a novel mechanical
response in which the work of indentation is transmitted almost solely to the
liquid, rather than to the floating film. We attribute this unique response to
a nontrivial isometry attained by the deformed film, and discuss the scaling
laws and the relevance of similar isometries to other systems in which a
confined sheet is subjected to weak tensile loads.
