Abstract:
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.