AI 中文总结
本文证明Kwasik-Schultz构造的不可完全化开4维流形，其与不可去悬挂的$C_2$-作用相关的版本存在有限维紧ANR $\text{Z}$紧化，从而得到非伪可领的$\text{Z}$可紧化开4维流形，解答了相关问题。
AI 中文摘要
Kwasik与Schultz构造了满足无穷远处通常有限性与稳定性条件的两端开4维流形，但不允许任意小的1-邻域；特别地，其两端均不可领，故该流形不可完全化。本文证明，与其不可去悬挂的$C_2$-作用相关的开流形，仍存在有限维紧ANR $\boldsymbol{\text{Z}}$紧化。因此存在一个非伪可领的$\boldsymbol{\text{Z}}$可紧化开4维流形，回答了Guilbault与Tinsley提出的问题。
英文摘要
Kwasik and Schultz constructed two-ended open $4$-manifolds which satisfy the usual finiteness and stability conditions at infinity but do not admit arbitrarily small $1$-neighborhoods. In particular, neither end is collarable, so the manifolds are not completable. We show that the open manifolds associated to their non-desuspendable $C_2$-actions nevertheless admit finite-dimensional compact ANR $\mathcal{Z}$-compactifications. Consequently, there exists a $\mathcal{Z}$-compactifiable open $4$-manifold which is not pseudo-collarable. This answers a question of Guilbault and Tinsley.
Comments22 pages, no figures
