Concordance cosmology points to a universe of zero mean curvature, due to the inflation mechanism which occurred soon after the big bang, while along a relatively small number of lower redshift light paths where lensing events are observed, space is positively curved. How do we know that geometry and topology are robust rather than in a state of chaos? The phenomenon of cosmic shear provides an effective way of mapping curvature fluctuations, because it affects any light rays whether they intercept mass clumps or not. Moreover, shear depends to lowest order only on the total mass density of clumps and not on their mass function. We discuss a range of astrophysical applications of the principal manifestation of shear—the distortion of images. It will be shown that the quickest way of testing the existence of shear in the near universe is to look at the shape of Einstein rings. The fact that most of these rings are circular to a large extent means, statistically speaking, shear occurs at a much lower level than the expectation based on our current understanding of the inhomogeneous universe. While inflation may account for the mean geometry, it offers no means of stabilizing it against the fluctuations caused by nonlinear matter clumping at low redshift. Either this clumping is actually much less severe or the physical mechanism responsible for shaping the large-scale curvature has been active not only during the very early epochs, but also at all subsequent times. Might it be the vital "interface" between expansion on Hubble distances and gravity on cluster scales and beneath?
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