A Complex of Incompressible Surfaces for handlebodies and the Mapping Class Group

摘要

For a genus g handlebody H a simplicial complex, with vertices being isotopyclasses of certain incompressible surfaces in H, is constructed and severalproperties are established. In particular, this complex naturally contains, asa subcomplex, the complex of curves of the boundary surface of H. As in theclassical theory, the group of automorphisms of this complex is identified withthe mapping class group of the handlebody.