A Faithful Action of the Mapping Class Group $\mathrm{Mod}(S_g)$ on the $(2g-1)$-Sphere

Abstract

We prove that $\mathrm{Mod}(S_g)$ acts faithfully by orientation-preserving homeomorphisms on a $(2g-1)$-sphere when $g \geq 3$ using equivariant blow-up and bi-orderability of the Torelli group.