A complex of incompressible surfaces for handlebodies and the mapping class group

摘要

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.