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Results tagged with chern-classes
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user 318
Characteristic classes associated to complex vector bundles.
15
votes
Accepted
Why is the first chern class of a line bundle $c_1(L) = 1-L$ in complex K-theory?
This comes from the choice of the $K$-theory Thom class for complex vector bundles.
Firstly, recall that $K$-theory $K^0(X)$ can be described as the group of bounded chain complexes of vector bundles …
- 18.2k
31
votes
Does a "Chern character" exist for any generalized cohomology theory?
For any (connective) spectrum $E$ one may rationalise it to get a rational spectrum $E_\mathbb{Q}$, and a map $E \to E_\mathbb{Q}$. Now rational spectra split as wedges of Eilenberg-Mac Lane spectra, …
- 18.2k