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Fibered faces and the dynamics of mapping classes in special subgroups of the mapping class group. |
| Abstract: |
| Lecture 1: We introduce basic properties of pseudo-Anosov mapping classes and how they correspond to integral points on fibered faces. Properties of Alexander and Teichmueller polynomials as developed by C. McMullen will be reviewed, and examples and applications will be given. |
| Lecture 2: We use covering spaces to describe families of fibrations of a given 3-manifold associated to rational points on a fibered face, and describe the behavior of the monodromy of the fibrations. If the 3-manifold is hyperbolic, then the monodromies of fibrations are pseudo-Anosov. We give some detailed examples of mapping classes associated to converging points on a fibered face. |
| Lecture 3: We study the locus on fibered faces of certain special subgroups of the mapping class group, and give applications concerning dynamics of mapping classes in special subgroups of the mapping class groups for surfaces of varying genus. |