Injections of the complex of separating curves into the Torelli complex

2009/11/19 by Yoshikata Kida, Kida, Yoshikata
Mathematics · #20E36 #20F38 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0911.3926

openalex publication_date 2009/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Generating the Torelli group
• Superinjective Simplicial Maps of Complexes of Curves and Injective Homomorphisms of Subgroups of Mapping Class Groups II
• The Torelli geometry and its applications
• Curve complex as a coset intersection complex
• Complexes of Nonseparating Curves and Mapping Class Groups