Combinatorial rigidity in curve complexes and mapping class groups

Kenneth J. Shackleton

Vol. 230 (2007), No. 1, 217–232

DOI: 10.2140/pjm.2007.230.217

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 property for mapping class groups.

Keywords

curve complex, mapping class group

Mathematical Subject Classification 2000

Primary: 57M50

Secondary: 20F38

Milestones

Received: 27 July 2005

Accepted: 17 April 2006

Published: 1 March 2007