All Questions

Let $L_1$ and $L_2$ be two nonintersecting picewise-linear or smooth knots in $\mathbb R^3$. Suppose they are ambient isotopic. Does there exist an embedded surface $f: S^1\times[0,1]\to \mathbb R^3$ ...

Given two $C^1$ immersed curves $f, g: S^1 \to {\mathbb R}^3$ with disjoint image, I would like a simple proof, working only in the smooth category, that there exists a unit direction $y \in {\mathbb ...

We like to ask for the comparison of two topologies of three 2-tori inside the same 4-manifolds glued from two different diffeomorphisms (see the end). Given an embedded torus $T$ with trivial normal ...