发表机构
Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences; State Key Laboratory of Mathematical Sciences & Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences; School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院数学与系统科学研究院; 中国科学院数学与系统科学研究院数学科学国家重点实验室; 中国科学院大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文改进了Brown的扭曲张量积，为道路连通基上的Serre纤维化构造了半自由上链模型，并证明了该模型在纤维同调有限维且基本群作用幂零时成立，推广了单连通基的经典结果。
AI 中文摘要
我们为以任意域为系数、基空间为道路连通空间的Serre纤维化构造上链模型。我们的构造改进了Brown的扭曲张量积，从而在基的奇异上链代数上产生一个微分分次模模型。若纤维的同调在每个次数上都是有限维的，且基的基本群在其上的作用是逐次幂零的，则该模型是由纤维的上同调生成的半自由分解。这推广了单连通基的经典构造。作为应用，我们将所得模型与任意半自由分解进行比较，表明每个这样的分解在基变换到基点后都能恢复纤维的上同调，并获得了相关谱序列崩溃所在页的一个显式界。
英文摘要
We construct cochain models for Serre fibrations over path-connected bases with coefficients in an arbitrary field. Our construction refines Brown's twisted tensor product to produce a differential graded module model over the singular cochain algebra of the base. If the homology of the fibre is finite dimensional in each degree and on which the action of the fundamental group of the base is degreewise nilpotent, then this model is a semifree resolution generated by the cohomology of the fibre. This extends the classical construction for simply connected bases. As applications, we compare the resulting model with arbitrary semifree resolutions, showing that every such resolution recovers the cohomology of the fibre after base change to the basepoint, and obtain an explicit bound on the page at which an associated spectral sequence collapses.
