On the topology of stable Lagrangian maps with singularities of types $A$ and $D$
Izvestiya. Mathematics , Tome 79 (2015) no. 3, pp. 581-622
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We study the topology of adjacencies of multisingularities in the image
of a stable Lagrangian map with singularities of types
$A_\mu^\pm$ and $D_\mu^\pm$.
In particular, we prove that each connected component
of the manifold of multisingularities of any fixed type
$A_{\mu_1}^{\pm}\dotsb A_{\mu_p}^{\pm}$ for a germ of the image of
a Lagrangian map with a monosingularity of type $D_\mu^\pm$ is
either contractible or homotopy equivalent to a circle. We calculate
the number of connected components of each kind for all types
of multisingularities. As a corollary, we obtain new conditions for
the coexistence of Lagrangian singularities.
Keywords:
stable Lagrangian maps, multisingularities, adjacency index, Euler characteristic.
@article{IM2_2015_79_3_a5,
author = {V. D. Sedykh},
title = {On the topology of stable {Lagrangian} maps with singularities of types $A$ and $D$},
journal = {Izvestiya. Mathematics },
pages = {581--622},
publisher = {mathdoc},
volume = {79},
number = {3},
year = {2015},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_2015_79_3_a5/}
}
V. D. Sedykh. On the topology of stable Lagrangian maps with singularities of types $A$ and $D$. Izvestiya. Mathematics , Tome 79 (2015) no. 3, pp. 581-622. http://geodesic.mathdoc.fr/item/IM2_2015_79_3_a5/