同伦转移余圈
Homotopy Transition Cocycles
摘要：
对于局部同伦平凡纤维化，可以定义转移函数$$ g\dab : U\da\cap U\db \to H = H(F)$$，其中$$ g\dab : U\da\cap U\db \to H = H(F)$$是$F$与自身的同伦等价的幺半群，但是，代替上循环条件，人们只得到$g\dab g\dbgam$与$g\dagam$同伦，作为$U\da\cap U\db\cap U\dgam$到$H$的映射。此外，在多个交叉点上，出现了更高的同伦，并且与纤维化的分类有关。完整的理论是由第一作者在他1965年的巴黎圣母院论文\cite{wirth:diss}中提出的。在这里，我们使用在此期间开发的语言来介绍它。我们还展示了如何这点的方向'超越格贝斯'。
英文摘要：
For locally homotopy trivial fibrations, one can define transition functions $$ g\dab : U\da\cap U\db \to H = H(F)$$ where $H$ is the monoid of homotopy equivalences of $F$ to itself but, instead of the cocycle condition, one obtains only that $g\dab g\dbgam$ is homotopic to $g\dagam$ as a map of $U\da\cap U\db\cap U\dgam$ into $H$. Moreover on multiple intersections, higher homotopies arise and are relevant to classifying the fibration. The full theory was worked out by the first author in his 1965 Notre Dame thesis \cite{wirth:diss}. Here we present it using language that has been developed in the interim. We also show how this points a direction `on beyond gerbes'.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
