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Automorphisms of the Torelli complex and the complex of separating curves. (English) Zbl 1378.57027
Summary: We compute the automorphism groups of the Torelli complex and the complex of separating curves for all but finitely many compact orientable surfaces. As an application, we show that the abstract commensurators of the Torelli group and the Johnson kernel for such surfaces are naturally isomorphic to the extended mapping class group.

##### MSC:
 57M99 General low-dimensional topology 57S05 Topological properties of groups of homeomorphisms or diffeomorphisms 20F38 Other groups related to topology or analysis 57M07 Topological methods in group theory 57N05 Topology of the Euclidean $$2$$-space, $$2$$-manifolds (MSC2010)
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