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The images of distant galaxies are magnified and sheared by mass fluctuations
encountered along the line of sight. Shear fields due to weak gravitational lensing have characteristic coherent patterns. We describe the topological defects in the shear field in terms of the curvature of an imaginary surface whose height function is given by the lensing potential. The resulting defects can then be identified as umbilical points of the potential surface produced by ellipsoidal halos. This enables to infer the correlation function of the lensing potential at large redshifts by measuring the abundance of defects in shear maps.