Quasi Semi-Border Singularities

Fawaz Alharbi and Suliman Alsaeed
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Fawaz Alharbi: Applied Science College, Department of Mathematical Sciences, Umm Al-Qura University, P.O. Box 715, 21955 Makkah, Saudi Arabia
Suliman Alsaeed: Applied Science College, Department of Mathematical Sciences, Umm Al-Qura University, P.O. Box 715, 21955 Makkah, Saudi Arabia

Mathematics, 2019, vol. 7, issue 6, 1-16

Abstract: We obtain a list of simple classes of singularities of function germs with respect to the quasi m -boundary equivalence relation, with m ≥ 2 . The results obtained in this paper are a natural extension of Zakalyukin’s work on the new non-standard equivalent relation. In spite of the rather artificial nature of the definitions, the quasi relations have very natural applications in symplectic geometry. In particular, they are used to classify singularities of Lagrangian projections equipped with a submanifold. The main method that is used in the classification is the standard Moser’s homotopy technique. In addition, we adopt the version of Arnold’s spectral sequence method, which is described in Lemma 2. Our main results are Theorem 4 on the classification of simple quasi classes, and Theorem 5 on the classification of Lagrangian submanifolds with smooth varieties. The brief description of the main results is given in the next section.

Keywords: singularity; quasi; semi-border; m-boundary; Lagrangian projection (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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