Let f : M → ℝ2 be a smooth map of a closed n-dimensional manifold (n ≥ 2) into the plane and let π2n+2: ℝn+2 → ℝ2 be an orthogonal projection. We say that / has the standard lifting property, if every embedding f̃ : ℝn+2 with π2n+2 o f̃= f is standard in a certain sense. In this paper we give some sufficient conditions for a generic smooth map / to have the standard lifting property when M is a closed surface or an n-dimensional homotopy sphere.
All Science Journal Classification (ASJC) codes
- Geometry and Topology