COMBINATORIAL RIGIDITY IN CURVE COMPLEXES AND MAPPING CLASS GROUPS

By K. Shackleton. 2005

71 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/666d544f5792a3403b6b6338ec17f8ac78d6fd80

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Injective simplicial maps of the arc complex (2006, background): “Shackleton proved that injective simplicial maps of the curve complex are induced by homeomorphisms in [21] (he also considers maps between different surfaces), and he obtained strong local co-Hopfian results for mapping class groups.”
Injections of mapping class groups (2008, methodology): “Automorphisms of mapping class groups ∗Partially supported by M.E.C. grant MTM2006/14688 †Partially supported by NSF grant DMS-0603881 ‡Partially supported by NSF grant DMS-0706878 and Alfred P. Sloan Foundation were classified by Ivanov [18], Korkmaz [23] and Luo [26]; and injections from finite in”
Injections of Artin groups (2005, unknown): “G R ] 1 7”
Curve Complexes and Finite Index Subgroups of Mapping Class Groups (2005, methodology): “He used it to show (in most cases) that any simplicial embedding of a curve complex into a curve complex of equal or lesser dimension is necessarily an automorphism [ 27 ].”