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

Charalampos Charitos; Ioannis Papadoperakis; Georgios Tsapogas

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arXiv · 1104.0660

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

Charalampos Charitos·Ioannis Papadoperakis·Georgios Tsapogas

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Abstract

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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Charalampos Charitos, Ioannis Papadoperakis, Georgios Tsapogas. 2011-04-04. A Complex of Incompressible Surfaces for handlebodies and the Mapping Class Group. https://arxiv.org/abs/1104.0660

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