Lecture Notes for Math 541 Spring 2018 - Bundles and Characterisic Classes

Note: These are my personal lecture notes. They may contain errors. Some of the previous lectures need to be rewritten so that they are more legible. I will add these later.

• Lecture 1 - Introduction
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• Lecture 11 - Principal G-bundles
• Lecture 12 - First Stiefel-Whitney class
• Lecture 13 - Grassmann manifolds
• Lecture 14 - The canonical bundle is universal
• Lecture 15 - The classification of vector bundles, part I
• Lecture 16 - The classification of vector bundles, part II
• Lecture 17 - The classification of vector bundles, part III
• Lecture 18 - The clutching construction
• Lecture 19 - Stiefel-Whitney classes
• Lecture 20 - Properties of Stiefel-Whitney classes
• Lecture 21 - Cell structure of the Grassmann, part I
• Lecture 22 - Cell structure of the Grassmann, part II
• Lecture 23 - Cohomology of the Grassmann, part I
• Lecture 24 - Cohomology of the Grassmann, part II
• Lecture 25 - Existence of Stiefel-Whitney classes
• Lecture 26 - Steenrod squares
• Lecture 27 - Applications of Stiefel-Whitney classes
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• Lecture 31 - Euler class
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• Lecture 33 - First Chern class

Handouts
• Notes on the equivalence of the two definitions of the first Stiefel-Whitney class