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Geometric subgroups of mapping class groups. (English) Zbl 1007.57014

The subgroups of the mapping class group of a marked Riemann surface induced from subsurfaces are intensively studied. After classifying the kernels of inclusion-induced maps of the mapping class groups of subsurfaces, the main result states that when the above kernel is trivial, the commensurability class of the image subgroup determines up to isotopy the defining subsurface. The centralizers, normalizers and commensurators of those image subgroups are also determined. The main devices of proofs are based on the system of simple closed curves on surfaces with associated Dehn twists (Thurston theory) and a simple lemma from D. B. A. Epstein’s paper [Acta Math. 115, 83-110 (1966; Zbl 0136.44605)].

MSC:

57M99 General low-dimensional topology
20F38 Other groups related to topology or analysis
57M60 Group actions on manifolds and cell complexes in low dimensions

Citations:

Zbl 0136.44605
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References:

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