Generalized Artin and Brauer induction for compact Lie groups

Fausk, Halvard

doi:10.1090/S0002-9947-08-04528-5

Generalized Artin and Brauer induction for compact Lie groups
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Trans. Amer. Math. Soc. 360 (2008), 5043-5066 Request permission

Abstract:

Let $G$ be a compact Lie group. We present two induction theorems for certain generalized $G$-equivariant cohomology theories. The theory applies to $G$-equivariant $K$-theory $K_G$, and to the Borel cohomology associated with any complex oriented cohomology theory. The coefficient ring of $K_G$ is the representation ring $R(G)$ of $G$. When $G$ is a finite group the induction theorems for $K_G$ coincide with the classical Artin and Brauer induction theorems for $R(G)$.

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