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Results tagged with chern-classes
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user 118688
Characteristic classes associated to complex vector bundles.
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 $ …
- 6,023
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
1
vote
Accepted
determinant of curvature (notation issue)
Curvature $\Omega$ is a $\mathfrak{g}$ valued $2$-form on $P$ i.e., for each $p\in P$, we have $\Omega(p):T_pP\times T_pP\rightarrow \mathfrak{g}$.
As $\mathfrak{g}$ is $\mathfrak{gl}(r,\mathbb{C})$ …
1
vote
1
answer
213
views
determinant of curvature (notation issue)
This is when studying about Chern classes from Kobayashi and Nomizu.
Let $\pi:E\rightarrow M$ be a complex vector bundle with fibre $\mathbb{C}^r$ and Group $G=GL(r,\mathbb{C})$.
Let $p:P\rightarrow …
- 6,023