Minimal Sets of Involution Generators for Big Mapping Class Groups

Abstract: Let $S(n)$, for $n \in \mathbb{N}$, be the infinite-type surface of infinite genus with $n$ ends, each of which is accumulated by genus. The mapping class groups of these types of surfaces are not countably generated. However, they are Polish groups, so they can be topologically countably generated. This paper focuses on finding minimal topological generating sets of involutions for $\mathrm{Map}(S(n))$. We establish that for $n \geq 16$, $\mathrm{Map}(S(n))$ can be topologically generated by four involutions. Furthermore, we establish that the the mapping class groups of the Loch Ness Monster surface ($n=1$) and the Jacob's Ladder surface ($n=2$) can be topologically generated by three involutions.