Geometry of universal magnification invariants

Recent work in gravitational lensing and catastrophe theory has shown that the sum of the signed magnifications of images near folds, cusps, and also higher catastrophes is zero. Here, it is discussed how Lefschetz fixed point theory can be used to interpret this result geometrically for a subfamily of these catastrophes, namely, the generic case of folds, cusps, elliptic and hyperbolic umbilics, swallowtails, and the elliptic and hyperbolic umbilics in gravitational lensing. (C) 2009 American Institute of Physics. [DOI: 10.1063/1.3204970]