Let $S$ be a connected, compact and orientable surface of genus two having exactly one boundary component. We describe any automorphism of the Torelli complex of $S$, and describe any automorphism of the Torelli group of $S$. More generally, we study superinjective maps from the Torelli complex of $S$ into itself, and show that any finite index subgroup of the Torelli group of $S$ is co-Hopfian.
"Automorphisms of the Torelli Complex for the One-holed Genus Two Surface." Tokyo J. Math. 37 (2) 335 - 372, December 2014. https://doi.org/10.3836/tjm/1422452797