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A Relative Form of Equivalent K-Theory

Toshimitsu Matsuda

1971Institutional Repositories DataBase (IRDB)Mathematics被引 1开放获取

摘要

Intreduction.Let G be a compact Lie group, T a maximal torusof G, 9V(G) the Weyl group of G and X a compact G-space.Then the following results on the equivariant KJ-theory will be required from [1] and[2].Tkeorem (A).(i) VVe have a ring homomorphism R(G)--->R(T) (by the restriction maP) which is inj'ective.R(G) maPs (biiectively) onto the ring of invariants.ofR(T) under the action of VV(G).(ii) The sequence O-Kt,*(X) >K.*(X) is sPlit exact.((i) is obtained from 4. 4 of [1] and (ii) from ProPosition (4, 9) of [2], ) Now the aim of this paper is to prove the fol!owing Theorem: Theorem (B).VVe have the following sPlit exact sequences: OoK*.(X) >K:k.(X)--)pK*(G,T)(X)-OO -K*a(X) -K*T(X)W(G) --:->-K

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