AI 中文总结
本文针对奇素数p，研究具有基本群ℤ/p ⋊ ℤ的闭4维流形的同伦分类，确定其同伦型的判定依据，推广了Hambleton–Kreck的相关结果并证明了普适性分类部分结论。
AI 中文摘要
对于奇素数p，本文证明具有基本群ℤ/p ⋊ ℤ的闭4维流形的同伦型由其二次2型及一个附加的ℤ/p值相交形式确定。本文还将Hambleton–Kreck关于庞加莱4复形的极化同伦分类的结果推广到无限群，并证明了一些更具普适性的同伦分类部分结果。
英文摘要
For an odd prime $p$, we show that the homotopy type of a closed $4$-manifold with fundamental group $\mathbb{Z}/p \rtimes \mathbb{Z}$ is determined by its quadratic $2$-type together with an additional $\mathbb{Z}/p$-valued intersection form. We also give a generalization to infinite groups of a result of Hambleton--Kreck on the polarized homotopy classification of Poincaré $4$-complexes, and we prove some partial results on the homotopy classification that are applicable more generally.
Comments24 pages
