Embedded totally geodesic surfaces in fully augmented links

Abstract

This paper studies embedded totally geodesic surfaces in fully augmented link complements. Not surprisingly, there are no closed embedded totally geodesic surfaces. Non-compact surfaces disjoint from crossing disks are seen to be punctured spheres orthogonal to the standard cell decomposition, while those that intersect crossing disks do so in very restricted ways. Finally we show there is an augmentation of any checkerboard surface in which that surface becomes totally geodesic.