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What is the centralizer of a pseudo-Anosov element in the mapping class group of an orientable punctured surface? Is it cyclic? If so, where can I find a proof?

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See McCarthy's paper And here are some more characters.

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  • $\begingroup$ In more detail, the centralizer is virtually cyclic but is not cyclic in general. $\endgroup$
    – Misha
    Nov 11, 2013 at 14:04

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