On the topology of stable Lagrangian maps with singularities of types A and D

摘要

We study the topology of adjacencies of multisingularities in the image of a stable Lagrangian map with singularities of types A(mu)(+/-) and D-mu(+/-). In particular, we prove that each connected component of the manifold of multisingularities of any fixed type A(mu 1)(perpendicular to) . . . A(mu p)(+/-) for a germ of the image of a Lagrangian map with a monosingularity of type D-mu(+/-) 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.