Some notes on the sectional fibrations

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• 作者：Ruizhi Huang ^{hrzsea@mail.nankai.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Xiugui Liu ; ¹ ; ^{xgliu@nankai.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：55P62
• 刊名：Topology and its Applications
• 出版年：2016
• 出版时间：1 July 2016
• 年：2016
• 卷：207
• 期：Complete
• 页码：123-135
• 全文大小：339 K

文摘

Given a fibration $F\hookrightarrow E\stackrel{p}{⟶}B$, we study its rational sections from three different points of view.

First, we transform the problem to some realization problems under different conditions, and also give some general criterion using the derivations of the Sullivan model of the fibre.

In addition, we consider the problem with the base space being a formal space. It turns out that the existence of a section is equivalent to the realization of some commutative differential graded algebra constructed from the minimal model of p.

Finally, we construct a Lie model for the space of the sections of p using the localization method, which is also used to study the sections of Lie epimorphisms.