Abstract
For a genus g handlebody H g a simplicial complex, with vertices being isotopy classes of certain incompressible surfaces in H g , is constructed and several properties are established. In particular, this complex naturally contains, as a subcomplex, the complex of curves of the surface \({\partial H_{g}}\). As in the classical theory, the group of automorphisms of this complex is identified with the mapping class group of the handlebody.
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Charitos, C., Papadoperakis, I. & Tsapogas, G. A complex of incompressible surfaces for handlebodies and the mapping class group. Monatsh Math 167, 405–415 (2012). https://doi.org/10.1007/s00605-012-0379-8
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DOI: https://doi.org/10.1007/s00605-012-0379-8