#### Volume 19, issue 1 (2019)

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Distortion of surfaces in graph manifolds

### G Christopher Hruska and Hoang Thanh Nguyen

Algebraic & Geometric Topology 19 (2019) 363–395
##### Abstract

Let $S↬N$ 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 (ie separable) and is exponentially distorted when the surface is not virtually embedded.

##### Keywords
graph manifold, separable subgroup, distortion
##### Mathematical Subject Classification 2010
Primary: 20F65, 20F67, 57M50