Injections of the complex of separating curves into the Torelli complex

Abstract

We show that for all but finitely many compact orientable surfaces, any superinjective map from the complex of separating curves into the Torelli complex is induced by an element of the extended mapping class group. As an application, we prove that any injective homomorphism from a finite index subgroup of the Johnson kernel into the Torelli group for such a surface is induced by an element of the extended mapping class group.

41 pages, 17 figures, organization rearranged

References in corpus (3)

• Automorphisms of Torelli groups
• The co-Hopfian property of the Johnson kernel and the Torelli group
• Automorphisms of the Torelli complex for the one-holed genus two surface

Cited by in corpus (1)

• Simplicial Maps of the Complexes of Curves on Nonorientable Surfaces