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1. Zhang, Hainan. Topology of fiber bundles.

Degree: MS, Department of Mathematics, 2014, Kansas State University

This report introduces the fiber bundles. It includes the definitions of fiber bundles such as vector bundles and principal bundles, with some interesting examples. Reduction of the structure groups, and covering homotopy theorem and some specific computation using obstruction classes, Cech cohomology, Stiefel-Whitney classes, and first Chern classes are included. Advisors/Committee Members: David Auckly.

Subjects/Keywords: Introduction to Fiber Bundles; obstruction theory from characteristic class; 1st SW class and 1st Chern class; Mathematics (0405)

…case, the 1st Chern class c1 (E) is defined to be the is an element in CCW… …extendable if and only if the 1st Stiefel-Whitney class w1σ (E) ∈ H1 (X, Z2 )… …x28;2). The 1st Stiefel-Whitney class is independent of the choice of sections. Let’s… …w1σ − w1τ = 0 (6.5) Figure 6.2: 1st Stiefel Class of total space E Exercise 1… …Figure 6.3: 1st Stiefel Class of total space E 0 Exercise 2. Compute w1σ (E 0 ) and… 

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APA (6th Edition):

Zhang, H. (2014). Topology of fiber bundles. (Masters Thesis). Kansas State University. Retrieved from

Chicago Manual of Style (16th Edition):

Zhang, Hainan. “Topology of fiber bundles.” 2014. Masters Thesis, Kansas State University. Accessed July 10, 2020.

MLA Handbook (7th Edition):

Zhang, Hainan. “Topology of fiber bundles.” 2014. Web. 10 Jul 2020.


Zhang H. Topology of fiber bundles. [Internet] [Masters thesis]. Kansas State University; 2014. [cited 2020 Jul 10]. Available from:

Council of Science Editors:

Zhang H. Topology of fiber bundles. [Masters Thesis]. Kansas State University; 2014. Available from: