The calculus of embeddings, due to Goodwillie, Klein, and Weiss, can be applied in multiple ways to the study of knot spaces. In this talk, I will focus on two applications - a homology spectral sequence and the construction of finite type knot invariants. First, I will give a spectral sequence due to Sinha and a simplification of the first differential, a first step in finding a more geometric interpretation of the spectral sequence. Second, I will describe results necessary for a method of constructing finite type invariants over the integers. |