Timeline for Characteristic classes in generalized cohomology theories?
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| Aug 18, 2010 at 23:17 | comment | added | Robert Bruner | In K-theory you have $c_1(L\otimes M) = c_1(L) + c_1(M) - v c_1(L) c_1(M)$ where $v \in K^{−2}=K_2$ is the Bott class. This is the multiplicative group in the sense that $(1- v c_1(L \otimes M)) = (1 - v c_1(L)) (1 - v c_1(M))$ There are other normalizations: $1+ v c_1(L)$ gives all plus signs and in periodic K-theory we could just work in $K^0$, or equiv, set $v=1$. The form I wrote has the virtue of linking Chern classes in cohomology, connective K-theory, and periodic K-theory: the Chern classes in connective K-theory specialize to those in ordinary cohomology and in periodic K-theory. | |
| Dec 24, 2009 at 15:27 | history | answered | Andrea Ferretti | CC BY-SA 2.5 |