Mapping Class Groups

Abstract

In this chapter, we shift the focus to exotic actions of mapping class groups on the circle, where here “exotic” means “not conjugate to Nielsen’s standard action” (see Handel and Thurston (Adv Math 56:173–191, 1985) and Casson and Bleiler (Automorphisms of Surfaces After Nielsen and Thurston, Cambridge University Press, Cambridge, 1988) for detailed discussions of Nielsen’s action). We first discuss actions of fibered, hyperbolic 3-manifold groups on S1, in relation to Nielsen’s action.