Distortion of surfaces in graph manifolds
arXiv:1703.07458 · doi:10.2140/agt.2019.19.363
Abstract
Let S be an immersed horizontal surface in a 3-dimensional graph manifold. We show that the fundamental group of the surface S is quadratically distorted whenever the surface is virtually embedded (i.e., separable) and is exponentially distorted when the surface is not virtually embedded.
29 pages, 2 figures