Geometry of Universal Magnification Invariants

Abstract

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. It is shown for the generic case as well as for elliptic and hyperbolic umbilics in gravitational lensing.