分野別セミナー

A smooth map between smooth manifolds is called a special generic map if it has only definite fold points as its singularities. We say that a smooth map of a manifold into R^p lifts to R^k, k > p, if it factors as the composition of an immersion or an embedding into R^k and a standard projection R^k -> R^p. In this talk, we first give a necessary and sufficient condition for a special generic map of a closed simply connected manifold of dimension 5 or 6 into R^3 to lift to a codimension one embedding in terms of the singular point set. Furthermore, we show that a special generic map of a closed orientable manifold of dimension n > 6 into R^3 lifts to an embedding into R^k for k > (3n+2)/2 if the normal bundle of the singular point set is trivial.