Arnold's seminar

March, 30

M.Kazarian,  Elementary introduction to the theory of
             characteristic classes dual to singularity loci


Theorems of global singularity theory express topological invariants
in terms of singularities of some differential objects: mapping germs,
morphisms of bundles, RC-singularities etc. The classical example
is Hopf theorem which relates the Euler characteristic of a smooth
manifold in terms of singular points of a vector field on it.
We present basic ideas and methods of this theory.
Among the new results we present new Giambelli type formulas obtained
with B.Shapiro for classes dual to degeneracy loci for distributions
on smooth manifolds. The computation is based on the study of
combinatorics of certain Hall bases in free Lie algebras.