BNSR-Invariants of Surface Houghton Groups

Noah Torgerson; Jeremy West

doi:10.2140/agt.2025.25.4897

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arXiv · 2403.04941

BNSR-Invariants of Surface Houghton Groups

Noah Torgerson·Jeremy West

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Abstract

The surface Houghton groups $\mathcal{H}_{n}$ are a family of groups generalizing Houghton groups $H_n$, which are constructed as asymptotically rigid mapping class groups. We give a complete computation of the BNSR-invariants $Σ^{m}(P\mathcal{H}_{n})$ of their intersection with the pure mapping class group. To do so, we prove that the associated Stein--Farley cube complex is CAT(0), and we adapt Zaremsky's method for computing the BNSR-invariants of the Houghton groups. As a consequence, we give a criterion for when subgroups of $H_n$ and $P\mathcal{H}_{n}$ having the same finiteness length as their parent group are finite index. We also discuss the failure of some of these groups to be co-Hopfian.

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BibTeX RIS

Noah Torgerson, Jeremy West. 2025-09-18. BNSR-Invariants of Surface Houghton Groups. https://doi.org/10.2140/agt.2025.25.4897

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