Atoroidal surface bundles

Abstract

We show that there is a type-preserving homomorphism from the fundamental group of the figure-eight knot complement to the mapping class group of the three-punctured torus. As a corollary, we obtain infinitely many commensurability classes of purely pseudo-Anosov surface subgroups of mapping class groups of closed surfaces. This gives the first examples of compact aspherical atoroidal surface bundles over surfaces

Authors

Autumn E. Kent

Department of Mathematics, University of Wisconsin, Madison, WI

Christopher J. Leininger

Department of Mathematics, Rice University, Houston, TX