KO-Characteristic classes
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(Created page with '== KO-Pontryagin classes == <wikitex>; The KO-Pontryagin classes $\pi^j$ are defined by setting $\pi^0(L) = 1, \pi^1(L)=L-2, \pi^j(L) = 0$ for $j \ge 2$ for complex line bundles…')
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(Created page with '== KO-Pontryagin classes == <wikitex>; The KO-Pontryagin classes $\pi^j$ are defined by setting $\pi^0(L) = 1, \pi^1(L)=L-2, \pi^j(L) = 0$ for $j \ge 2$ for complex line bundles…')
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Revision as of 12:30, 27 January 2010
KO-Pontryagin classes
The KO-Pontryagin classes are defined by setting for for complex line bundles L and then requiring naturality and where . Here and are oriented bundles. In fact, these properties determine because the group injects into under the complexification of the map which is induced by the restriction to the maximal torus (compare [Anderson&Brown&Peterson1966]). For we set and . Such a class gives a map .
References
- [Anderson&Brown&Peterson1966] D. W. Anderson, E. H. Brown and F. P. Peterson, Spin cobordism, Bull. Amer. Math. Soc. 72 (1966), 256–260. MR0190939 (32 #8349) Zbl 0156.21605
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