Automorphisms of the Torelli complex for the one-holed genus two surface

Abstract

Let S be a connected, compact and orientable surface of genus two having exactly one boundary component. We study automorphisms of the Torelli complex for S, and describe any isomorphism between finite index subgroups of the Torelli group for S. More generally, we study superinjective maps from the Torelli complex for S into itself, and show that any finite index subgroup of the Torelli group for S is co-Hopfian.

28 pages, 21 figures. Proof was largely modified because some hexagons had been overlooked (v3), Figures added and exposition improved (v4)

References in corpus (5)

• A note on the connectivity of certain complexes associated to surfaces
• Automorphisms of Torelli groups
• Addendum to: Commensurations of the Johnson kernel
• Automorphisms of the Torelli complex and the complex of separating curves
• The co-Hopfian property of the Johnson kernel and the Torelli group

Cited by in corpus (3)

• OE and W* superrigidity results for actions by surface braid groups
• Injections of the complex of separating curves into the Torelli complex
• Simplicial Maps of the Complexes of Curves on Nonorientable Surfaces