Cubulating drilled bundles over graphs

Mj, Mahan; Nag, Biswajit

doi:10.2140/agt.2025.25.4095

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ISSN (electronic): 1472-2739

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Cubulating drilled bundles over graphs

Mahan Mj and Biswajit Nag

Algebraic & Geometric Topology 25 (2025) 4095–4146

DOI: 10.2140/agt.2025.25.4095

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 $π_{1} (F)$ is relatively hyperbolic with $ℤ \oplus ℤ$ peripheral groups. Combining the relative hyperbolicity of $π_{1} (F)$ thus obtained with a theorem of Wise, we establish virtually special cubulability of $π_{1} (F)$ provided that the maximal undrilled subbundles of $F$ are cubulable.

Keywords

CAT(0) cube complex, surface bundle over graph, relative hyperbolicity, relatively quasiconvex hierarchy

Mathematical Subject Classification

Primary: 20F65, 20F67

Secondary: 22E40, 57M50

References

Publication

Received: 11 December 2023

Revised: 15 August 2024

Accepted: 14 October 2024

Published: 29 October 2025

Authors

Mahan Mj
School of Mathematics Tata Institute of Fundamental Research Mumbai India

Biswajit Nag
School of Mathematics Tata Institute of Fundamental Research Mumbai India

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Volume 25, issue 7 (2025)