Cubulating drilled bundles over graphs
Mahan Mj, Biswajit Nag · Algebraic & Geometric Topology · 2025
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 1 .F / is relatively hyperbolic with Z ˚Z peripheral groups.Combining the relative hyperbolicity of 1 .F / thus obtained with a theorem of Wise, we establish virtually special cubulability of 1 .F / provided that the maximal undrilled subbundles of F are cubulable.20F65, 20F67; 22E40, 57M50 1. Introduction 4095 2. Bundles, drilled bundles, and graphs of groups 4100 3. Relative hyperbolicity 4101 4. Guessing geodesics 4118 5.