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.

RevTEX4, 13 pages, submitted to J. Math. Phys

References in corpus (3)

• A Universal Magnification Theorem for Higher-Order Caustic Singularities
• A Lefschetz fixed point theorem in gravitational lensing
• A Universal Magnification Theorem II. Generic Caustics up to Codimension Five

Cited by in corpus (6)

• Signed magnification sums for general spherical lenses
• Mathematics of Gravitational Lensing: Multiple Imaging and Magnification
• Strong lensing, plane gravitational waves and transient flashes
• Cusp Summations and Cusp Relations of Simple Quad Lenses
• Analytical Solutions of Singular Isothermal Quadrupole Lens
• The Magnification Invariant of Circularly-symmetric Lens Models