Combinatorial rigidity in curve complexes and mapping class groups

2005/03/10 by Shackleton, Kenneth J.
#20F38 #57M50 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.math/0503199

Abstract

In all possible cases, we prove that local embeddings between two curve complexes whose complexities do not increase from domain to codomain are induced by surface homeomorphism. This is our first main result. From this we can deduce our second, a strong local co-Hopfian result for mapping class groups.

Related

• Finite rigid sets in curve complexes
• Geometry and rigidity of mapping class groups
• Finite Rigid Sets in Curve Complexes of Non-Orientable Surfaces
• Curve complex as a coset intersection complex
• Finite rigid sets in sphere complexes