For one-vertex tubular groups that are both CAT(0) and free-by-cyclic, virtual specialness always holds, yet cocompact cubulation often fails; three related open questions are answered negatively.
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Some questions related to free-by-cyclic groups and tubular groups
For one-vertex tubular groups that are both CAT(0) and free-by-cyclic, virtual specialness always holds, yet cocompact cubulation often fails; three related open questions are answered negatively.