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arXiv · 2310.16403

Cubulating Drilled bundles over graphs

Mahan Mj·Biswajit Nag
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Abstract

We start with a Gromov-hyperbolic surface bundle $E$ over a graph, and drill out essential simple closed curves from fibers to obtain a drilled bundle $F$. We prove that for such drilled bundles $F$, the fundamental group $\pi_1(F)$ is relatively hyperbolic with $(\mathbb{Z}\oplus \mathbb{Z})$ peripheral groups. Combining the relative hyperbolicity of $\pi_1(F)$ thus obtained with a theorem of Wise, we establish virtually special cubulability of $\pi_1(F)$ provided that the maximal undrilled subbundles of $F$ are cubulable.

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Mahan Mj, Biswajit Nag. 2023-10-25. Cubulating Drilled bundles over graphs. https://doi.org/10.2140/agt.2025.25.4095

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