Automorphisms of the Torelli complex and the complex of separating curves

Abstract

We compute the automorphism groups of the Torelli complex and the complex of separating curves for all but finitely many compact orientable surfaces. As an application, we show that the abstract commensurators of the Torelli group and the Johnson kernel for such surfaces are naturally isomorphic to the extended mapping class group.

43 pages, 12 figures

References in corpus (2)

• Cutting and Pasting in the Torelli Group
• Addendum to: Commensurations of the Johnson kernel

Cited by in corpus (6)

• OE and W* superrigidity results for actions by surface braid groups
• Primeness results for von Neumann algebras associated with surface braid groups
• Automorphisms of the Torelli complex for the one-holed genus two surface
• Commensurators of surface braid groups
• The co-Hopfian property of surface braid groups
• Finite rigid sets of the non-separating curve complex