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研究生： 戴碧寬
Day, Biy-Kuang
論文名稱： 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
指導教授： 鄭志豪
Teh, Jyh Haur
口試委員: 潘戍衍
Pan, Shu-Yen
何南國
Ho, Nan Kuo
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
論文出版年： 2019
畢業學年度： 107
語文別： 英文
論文頁數： 34
中文關鍵詞： 宇纖維叢 、分類空間 、鄰域變形收縮 、拓樸群
外文關鍵詞： universal bundle, classifying, neighborhood, retract
相關次數： 點閱：1  下載：0 
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    • 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。

    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.

    1 Compactly generated topological groups 5 2 Milgram-Steenrod construction 7 3 Bar construction 16 4 The equivalent between two constructions 20 5 Neighborhood deformation retract and the fibration EG→BG 23 6 Neighborhood deformation retracts and brations 27

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