TL;DR
This paper explores the geometric interpretation of universal magnification invariants in gravitational lensing using Lefschetz fixed point theory, providing a unified framework for understanding image magnifications near catastrophes.
Contribution
It introduces a novel geometric interpretation of magnification invariants in gravitational lensing through Lefschetz fixed point theory, extending to various catastrophes.
Findings
Sum of signed magnifications near catastrophes is zero
Lefschetz fixed point theory offers a geometric understanding of magnification invariants
Results apply to generic cases and specific lensing catastrophes like elliptic and hyperbolic umbilics
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.
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