On Lagrangian and Legendrian singularities
type: Item
instance of: scholarly article
title: On Lagrangian and Legendrian singularities
zbMATH Open document ID: 1484.57027
published in: Arnold Mathematical Journal
publication date: 2021-12-16T00:00:00Z
review text: The paper under review is a brief survey of the author's results on the topology of adjacencies of stable simple multisingularities of Lagrangian and Legendrian maps. Among other things, the author reproduces from his earlier works the tables of adjacency indices of monosingularities to multisingularities for generic caustics in dimension \(n \leq 5\) and for generic wave fronts in dimension \(n\leq 6\) (see [\textit{V. D. Sedykh}, Izv. Math. 76, No. 2, 375--418 (2012; Zbl 1251.57021); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 76, No. 2, 171--214 (2012); ibid. 79, No. 3, 581--622 (2015; Zbl 1326.57049); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 79, No. 3, 159--202 (2015); ibid. 82, No. 3, 596--611 (2018; Zbl 1432.57059); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 82, No. 3, 154--169 (2018)].
reviewed by: Aleksandr G. Aleksandrov
Mathematics Subject Classification ID: 57R45
Mathematics Subject Classification ID: 53D35
Mathematics Subject Classification ID: 53D12
Mathematics Subject Classification ID: 58K05
Mathematics Subject Classification ID: 58K15
Mathematics Subject Classification ID: 57-02
Mathematics Subject Classification ID: 58-02
zbMATH DE Number: 7446995
zbMATH Keywords: survey
zbMATH Keywords: real singularities
zbMATH Keywords: Lagrangian maps
zbMATH Keywords: Legendrian maps
zbMATH Keywords: stable simple multisingularities
zbMATH Keywords: caustics
zbMATH Keywords: wave fronts
zbMATH Keywords: adjacency index
author: V. D. Sedykh
MaRDI profile type: Publication
full work available at URL: s40598-020-00161-9
OpenAlex ID: W3094252512
cites work: Q3997639
cites work: Q4193576
cites work: Q4773093
cites work: On the topology of wave fronts in spaces of low dimension
cites work: On the topology of stable Lagrangian maps with singularities of types $ A$ and $ D$
cites work: Topology of singularities of a stable real caustic germ of type $E_6$
cites work: Q3999261
DOI: 10.1007/S40598-020-00161-9
description: scientific article; zbMATH DE number 7446995