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Results tagged with characteristic-classes
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user 118688
Cohomology classes associated to vector bundles. Includes Stiefel-Whitney classes, Chern classes, Pontryagin classes, and the Euler class.
6
votes
0
answers
156
views
Geometric theory for cohomology groups $H^p(M;\mathbb{Z})$
An excerpt from the book Loop Spaces, Characteristic Classes and Geometric Quantization by Jean-Luc Brylinski is mentioned below:
Characteristic classes are certain cohomology classes associated
…
- 6,023
4
votes
1
answer
278
views
Chern -Weil map for topological principal G bundles
Let $G$ be a Lie group.
In the book Curvature and Characteristic classes, the author (Johan L. Dupont) mentiones in beginning of chapter 5 the following :
The notion of a topological principal $ …
- 35.5k
4
votes
0
answers
393
views
Chern-Weil theory and Weil homomorphism of principal bundle
In Kobayashi and Nomizu's book Foundations of Differential geometry they introduce the concept of connection on a principal $G$ bundle. In this book, they use connection on a principal bundle to defin …
- 6,023
2
votes
1
answer
442
views
Advantages of Atiyah sequence version of connections on a principal bundle
I am reading Lie Groupoids and Lie Algebroids in Differential Geometry
by Kirill Mackenzie.
In appendix (page $291$), before discussing about Atiyah sequence associated to a Principal bundle, the aut …
CommunityBot
- 1
3
votes
1
answer
573
views
How does one introduce characteristic classes [closed]
How does one introduce, or how were you introduced to characteristic classes?
You can assume that the student is comfortable with principal bundles and connections on principal bundles.
I am not as …
- 6,051
3
votes
1
answer
1k
views
Prerequisites for reading characteristic classes
Can some one tell me what are the prerequisites for learning characteristic classes as they are in book Foundations of Differential geometry by Kobayashi and Nomizu.
I only read first two chapters of …
- 1,005