On Lagrangian and Legendrian singularities (Q823814)

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)].