First Steps in Homotopy Results for Symplectic Embeddings of Ellipsoids

The space of symplectic embeddings of ellipsoids has been an object of great study in recent years. At this point, the existence and isotopy properties of this space have been well studied. In this dissertation, we take some first steps toward investigating the homotopy properties of the space of symplectic embeddings of ellipsoids. We identify a loop of symplectic embeddings E(a,b) U E(a,b) --> B^4(R) which is contractible when R > a+b and which is non-contractible when 2a < R < a+b, provided that b < 2a. We even show that this loop is not homologous to a constant map in the given range of R values.