Geodesic
On a real caustic of type $E_6$
Izvestiya. Mathematics, Tome 85 (2021) no. 2, pp. 279-305 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove that the manifold of non-singular points of a stable real caustic germ of type $E_6$ and the manifolds of points of transversal intersection of its smooth branches consist only of contractible connected components. We also calculate the number of these components.
Keywords: Lagrangian map, caustic, singularities of types $A$, multisingularities, adjacency index.
Mots-clés : $D$, $E$ 
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     title = {On a~real caustic of type $E_6$},
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V. D. Sedykh. On a real caustic of type $E_6$. Izvestiya. Mathematics, Tome 85 (2021) no. 2, pp. 279-305. http://geodesic.mathdoc.fr/item/IM2_2021_85_2_a4/

[1] V. I. Arnol'd, Singularities of caustics and wave fronts, Math. Appl. (Soviet Ser.), 62, Kluwer Acad. Publ., Dordrecht, 1990, xiv+259 pp. | DOI | MR | MR | Zbl | Zbl

[2] V. D. Sedykh, “On the topology of stable Lagrangian maps with singularities of types $A$ and $D$”, Izv. Math., 79:3 (2015), 581–622 | DOI | DOI | MR | Zbl

[3] V. D. Sedykh, “Topology of singularities of a stable real caustic germ of type $E_6$”, Izv. Math., 82:3 (2018), 596–611 | DOI | DOI | MR | Zbl

[4] V. A. Vasil'ev, Lagrange and Legendre characteristic classes, Adv. Stud. Contemp. Math., 3, Gordon and Breach Science Publishers, New York, 1988, x+268 pp. | MR | Zbl

[5] V. I. Arnold, A. N. Varchenko, S. M. Gusein-Zade, Osobennosti differentsiruemykh otobrazhenii, 3-e izd., MTsNMO, M., 2009, 672 pp.; V. I. Arnol'd, S. M. Gusein-Zade, A. N. Varchenko, Singularities of differentiable maps, С‚. I, Mod. Birkhäuser Class., Reprint of 1985 ed., Birkhäuser/Springer, New York, 2012, xii+382 СЃ. ; v. II, Reprint of 1988 ed., x+492 pp. | DOI | MR | Zbl | DOI | MR | Zbl