Atoroidal Surface Bundles

mapping class groups
moduli spaces
Surface bundles
hyperbolic 4-manifolds

Appears in collection : 2025 - T2 - WS2 - Low-dimensional phenomena: geometry and dynamics

I will discuss recent work with C. Leininger in which we produce purely pseudo-Anosov surface subgroups of mapping class groups, obtaining the first compact atoroidal surface bundles over surfaces. We do this by constructing a type-preserving representation of the figure eight knot group into the mapping class group of the thrice-punctured sphere.