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We consider a Chinese remainder theorem for (labeled) graphs. For $X$ a GKM$T$-variety and $Y$ an invariant subvariety, we use this to give a conditionfor surjectivity of the restriction map $H^*(X) \to H^*(Y)$. In particular,this applies to certain invariant subvarieties in a smooth toric variety.

Momentum graphs, Chinese remainder theorem and the surjectivity of the restriction map