Complements of caustics of real function singularities
V.A. Vassiliev
Journal of Singularities
volume 27 (2024), 47-67
Received: 26 August 2023. In revised form: 3 March 2024
Abstract:
We study the topology of complements of caustics of simple and parabolic function singularities, namely complete the enumeration of connected components of the complements of caustics of simple (in the sense of V. Arnold) singularities, in particular find the numbers of these components for the last two classes, E_7 and E_8, remaining unknown after the works of R. Thom, V. Arnold and V. Sedykh; represent all these components for simple singularities by explicitly constructed functions, and also realize their one-dimensional homology and cohomology groups by cycles and cocycles; prove that for some parabolic singularities the two-dimensional homology groups of the complements of their caustics are nontrivial.
2020 Mathematical Subject Classification:
14B07, 14Q30, 78A05
Key words and phrases:
Caustic, function singularity, versal deformation
Author(s) information:
V.A.Vassiliev
Weizmann Institute of Science
Department of Mathematics
Rehovot, Israel