Geodesic
Distortion of surfaces in graph manifolds
Hruska, Christopher1 ; Nguyen, Hoang1
1 Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI, United States
Algebraic and Geometric Topology, Tome 19 (2019) no. 1, pp. 363-395

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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.

DOI : 10.2140/agt.2019.19.363
Classification : 20F65, 20F67, 57M50
Keywords: graph manifold, separable subgroup, distortion

Hruska, Christopher 1 ; Nguyen, Hoang 1

1 Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI, United States 
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Hruska, Christopher; Nguyen, Hoang. Distortion of surfaces in graph manifolds. Algebraic and Geometric Topology, Tome 19 (2019) no. 1, pp. 363-395. doi: 10.2140/agt.2019.19.363

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