Minimal Sets of Generators for Big Mapping Class Groups

Abstract: Let $S(n)$ be the infinite-type surface with infinite genus and $n \in \mathbb{N}$ ends, all of which are accumulated by genus. The mapping class group of this surface, $\mod(S(n))$, is a Polish group that is not countably generated, but it is countably topologically generated. This paper focuses on finding minimal sets of generators for $\mod(S(n))$. We show that for $n \ge 8$, $\mod(S(n))$ is topologically generated by three elements, and for $n \ge 3$, $\mod(S(n))$ is topologically generated by four elements. We also establish a generating set of two elements for the Loch Ness Monster surface ($n=1$) and a generating set of three elements for the Jacob's Ladder surface ($n=2$).