Doubly Slice Montesinos Links

Abstract

In this paper, we compare the notions of double sliceness for links. The main result is showing that a large family of 2-component Montesinos links are not strongly doubly slice despite being weakly doubly slice and having doubly slice components. Our principal obstruction to strong double slicing comes by considering branched double covers. To this end, we prove a result classifying Seifert fibered spaces that admit a smooth embedding into integer homology ${\mathit{S}}^1\times {\mathit{S}}^3$s by maps inducing surjections on the first homology group. A number of other results and examples pertaining to doubly slice links are also given.