LIFTING A GENERIC MAP OF A SURFACE INTO THE PLANE TO AN EMBEDDING INTO 4-SPACE

摘要

Let f : M → R~2 be a stable map of a closed surface M into the plane and π_2~2: R~4 → R~2 the orthogonal projection. In this paper, we will show that for any such f there exists an embedding F : M → R~4 such that f = π_2~2 o F is satisfied.