Metrically un-knotted corank 1 singularities of surfaces in \(\mathbb {R}^4\) (Q1711070)

The paper studies semi-algebraic surface germs \((X, 0)\subset (\mathbb R^{4}, 0)\) defined as images of injective polynomial map germs \(F : (\mathbb R^{2}, 0) \to (\mathbb R^{4}, 0)\). Its main result is the following: if \((X, 0)\) is a normally embedded surface with isolated singularity, and if the 2-jet of \(F\) is \((x, xy, 0, 0)\), then the link of \((X, 0)\) is a trivial knot. The proof uses the projection of the surface to its tangent cone.