The maximal number of bushy free factors that coarsely embed into a standard HHS is the orthogonality number of its bushy domains; this distinguishes Torelli groups, Johnson kernels and surface braid groups.
Coarse obstructions to cocompact cubulation
2 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We provide geometric methods to give bounds on the large-scale dimension of CAT(0) cube complexes quasiisometric to a given group $G$. In situations where these bounds conflict we obtain obstructions to $G$ being cocompactly cubulated. More strongly, the obstructions prevent $G$ from being a coarse median space. As applications, we show that many free-by-cyclic groups cannot be cocompactly cubulated, even virtually, and prove that any tubular group with a coarse median is virtually compact special. We also exhibit a group that is CAT(0), $C(6)$, and virtually special, yet is not quasiisometric to any CAT(0) cube complex. This is the first example of a $C(6)$ group that cannot be cocompactly cubulated, resolving a question of Jankiewicz and partially answering a question of Wise.
representative citing papers
Free-by-cyclic groups with coarse medians are algebraically characterized by unbranched blocks in maximal virtually F_n x Z subgroups and excessive linearity of completely split relative train track maps.
citing papers explorer
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Coarse embeddings of products of trees as quasi-isometry invariants
The maximal number of bushy free factors that coarsely embed into a standard HHS is the orthogonality number of its bushy domains; this distinguishes Torelli groups, Johnson kernels and surface braid groups.
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Characterizing hierarchically hyperbolic free by cyclic groups
Free-by-cyclic groups with coarse medians are algebraically characterized by unbranched blocks in maximal virtually F_n x Z subgroups and excessive linearity of completely split relative train track maps.