兩種宇纖維叢構造方式的等同與分類空間的應用

An Equivalence between two Constructions of Universal Bundles and Applications of Classifying Spaces

戴碧寬(Biy-Kuang Day)

指導教授 ： 鄭志豪

國立清華大學/理學院/數學系/碩士(2019年)

摘要

本文將分別回顧米爾格倫－斯廷羅德宇纖維叢構造法以及柵欄宇纖維叢構造法，並且證明兩者同構。另一方面，在回顧宇纖維叢與鄰域變形收縮的關聯後，本文亦將證明當拓樸群對(G,Z)為鄰域變形收縮對時，其商映射G→G/Z會形成塞爾纖維叢。

關鍵字

宇纖維叢 ； 分類空間 ； 鄰域變形收縮 ； 拓樸群

並列摘要

This thesis reviews the Milgram-Steenrod construction and bar construction of universal bundles, and prove that these two constructions are equivalent. After reviewing relation between neighborhood deformation retract and the universal bundles, we prove that if a pair of topological group (G,Z) is a neighborhood deformation retract pair, then the quotient map G→G/Z is actually a Serre fibration.

並列關鍵字

universal bundle ； bundle ； classifying ； space ； neighborhood ； deformation ； retract

參考文獻

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