A knot is an embedding of a circle in a 3-sphere. The space of knots is the set of all knots, equipped with a topology. For simplicity, we focus on the space of long knots, i.e., a specific type of embedding of R^1 into R^3. In this space, the path components correspond exactly to the isotopy classes of long knots. I will describe the shape of each component up to homotopy, illustrated with examples.
