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

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

2011-04-04

arxiv.org/abs/1104.0660v1

Mathematics

Geometric Topology

12 pages, 3 figures

Scientific paper

For a genus g handlebody H a simplicial complex, with vertices being isotopy classes of certain incompressible surfaces in H, is constructed and several properties are established. In particular, this complex naturally contains, as a subcomplex, the complex of curves of the boundary surface of H. 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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