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arXiv · 1805.01094

Distortion of surfaces in 3-manifolds

Hoang Thanh Nguyen
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Abstract

Let $g \colon S \looparrowright N$ be a properly immersed $\pi_1$--injective surface in a non-geometric $3$--manifold $N$. We compute the distortion of $\pi_1(S)$ in $\pi_1(N)$ and show that how it is related to separability of $\pi_1(S)$ in $\pi_1(N)$. The only possibility of the distortion is linear, quadratic, exponential, and double exponential.

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Hoang Thanh Nguyen. 2018-05-03. Distortion of surfaces in 3-manifolds. https://doi.org/10.1112/topo.12114

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