Embedding Partial HNN Extensions In Ascending HNN Extensions

Daniel T. Wise; Hip Kuen Chong

Embedding Partial HNN Extensions In Ascending HNN Extensions

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arxiv 2408.00453 v1 pith:JWK7UPIP submitted 2024-08-01 math.GR

Hip Kuen Chong , Daniel T. Wise This is my paper · ORCID

classification math.GR

keywords ascendinggroupembedsextensionextensionsfreepartialactual

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We show that any partial ascending HNN extension of a free group embeds in an actual ascending HNN extension of a free group. Moreover, we can ensure that it embeds as the parabolic subgroup of a relatively hyperbolic group.

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Some questions related to free-by-cyclic groups and tubular groups
math.GR 2025-04 conditional novelty 7.0 of 10

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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