分野別セミナー

Let g be a continuous map between topological spaces.
Two points x, y in the source are defined to be equivalent if
g(x) = g(y) and they belong to the same connected component
of g^{-1}(g(x)) = g^{-1}(g(y)). The quotient space with respect
to this equivalence relation is called the Stein factorization
of g, which is not always a manifold, not even a polyhedron,
even if g is a smooth map between smooth manifolds.
In this talk, we show that if g is a proper C^\infty stable map,
then its Stein factorization is a polyhedron.