Houghton群的BNSR不变量得出结论，
The BNSR-invariants of the Houghton groups, concluded
摘要：
给出了Houghton群$H_n$的BNSR-不变量$Σ^m(H_n)$的完整计算.部分结果以前得到的作者，与一个猜想的全貌，我们现在确认。证明涉及到覆盖相关的$CAT(0)$立方体复形的相关子复形与某些局部凸子复形的交集，然后应用神经引理的强形式。完整计算的结果是，对于每个$1\le m\le n-1$，$H_n$允许到$\mathbb{Z}$的映射，其内核是$F_{m-1}$类型而不是$F_m$类型，而且没有这样的内核是$F_{n-1}$类型。
英文摘要：
We give a complete computation of the BNSR-invariants $Σ^m(H_n)$ of the Houghton groups $H_n$. Partial results were previously obtained by the author, with a conjecture about the full picture, which we now confirm. The proof involves covering relevant subcomplexes of an associated $CAT(0)$ cube complex by their intersections with certain locally convex subcomplexes, and then applying a strong form of the Nerve Lemma. A consequence of the full computation is that for each $1\le m\le n-1$, $H_n$ admits a map onto $\mathbb{Z}$ whose kernel is of type $F_{m-1}$ but not $F_m$, and moreover no such kernel is ever of type $F_{n-1}$.
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