Multiplane gravitational lensing. II. Global geometry of caustics

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Abstract
The global geometry of caustics due to a general multiplane gravitational lens system is investigated. Cusp-counting formulas and total curvatures are determined for individual caustics as well as whole caustic networks. The notion of light path obstruction points is fundamental in these studies. Lower bounds are found for such points and are used to get upper bounds for the total curvature. Curvature functions of caustics are also treated. All theorems obtained do not rely on the detailed nature of any specific potential assumed as a gravitational lens model, but on the overall differential-topological properties of general potentials. The methods employed are based on the following: Morse theory, projectivized rotation numbers, the Fabricius–Bjerre–Halpern formula, Whitney’s rotation number formula, Seifert decompositions, and the Gauss–Bonnet theorem.

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