Geodesic
Topology of singularities of a stable real caustic germ of type $E_6$
Izvestiya. Mathematics, Tome 82 (2018) no. 3, pp. 596-611 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study manifolds of singular points of a fixed type for a stable real caustic germ of type $E_6$. We prove the contractibility of every connected component of the manifold of singular points that are not points of transversal intersection of smooth branches of the caustic and calculate the number of these components.
Keywords: Lagrangian maps, caustics, simple singularities, multisingularities, Euler characteristic, adjacency index. 
@article{IM2_2018_82_3_a7,
     author = {V. D. Sedykh},
     title = {Topology of singularities of a~stable real caustic germ of type $E_6$},
     journal = {Izvestiya. Mathematics},
     pages = {596--611},
     year = {2018},
     volume = {82},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2018_82_3_a7/}
}
TY  - JOUR
AU  - V. D. Sedykh
TI  - Topology of singularities of a stable real caustic germ of type $E_6$
JO  - Izvestiya. Mathematics
PY  - 2018
SP  - 596
EP  - 611
VL  - 82
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/IM2_2018_82_3_a7/
LA  - en
ID  - IM2_2018_82_3_a7
ER  - 
%0 Journal Article
%A V. D. Sedykh
%T Topology of singularities of a stable real caustic germ of type $E_6$
%J Izvestiya. Mathematics
%D 2018
%P 596-611
%V 82
%N 3
%U http://geodesic.mathdoc.fr/item/IM2_2018_82_3_a7/
%G en
%F IM2_2018_82_3_a7
V. D. Sedykh. Topology of singularities of a stable real caustic germ of type $E_6$. Izvestiya. Mathematics, Tome 82 (2018) no. 3, pp. 596-611. http://geodesic.mathdoc.fr/item/IM2_2018_82_3_a7/

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

[2] E. Looijenga, “The discriminant of a real simple singularity”, Compositio Math., 37:1 (1978), 51–62 | MR | Zbl

[3] V. I. Arnold, Arnold's problems, Springer-Verlag, Berlin–Heidelberg; PHASIS, 2004, xvi+639 pp. | MR | MR | Zbl | Zbl

[4] V. A. Vasilev, Lagranzhevy i lezhandrovy kharakteristicheskie klassy, M., MTsNMO, 2000, 312 pp.

[5] 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

[6] J. Callahan, “Bifurcation geometry of $E_6$”, Math. Modelling, 1:4 (1980), 283–309 | DOI | MR | Zbl

[7] V. I. Arnol'd, S. M. Gusein-Zade, A. N. Varchenko, Singularities of differentiable maps, v. I, Monogr. Math., 82, The classification of critical points, caustics and wave fronts, Birkhäuser Boston, Inc., Boston, MA, 1985, xi+382 pp. | DOI | MR | MR | Zbl | Zbl