We prove two results about mutation invariance of link homology theories: Weshow that Khovanov's universal sl(2) homology is invariant under mutationand that the reduced sl(n) homology defined by Khovanov and Rozansky isinvariant under component-preserving positive mutation when n is odd. Wealso give a relationship between the Khovanov homology of a closed positive3-braid and the Khovanov homology of the braid after adding a number of fulltwists.
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