Am working on a problem for my grad math class, but I having some trouble intuitively understanding the idea of pseudo-Anosov mappings. I am trying to do something involving $a^{-1}b^{-1}ab$, where $a^{-1}b^{-1}ab=c$ for a pseudo-Anosov mapping $c$, but I don't know how to proceed, because I don't know what to say about $a$ and $b$. Are $a$ and $b$ necessarily pseudo-Anosov? I don't want to post the whole problem because I'd rather try to work through the rest myself. Please let me know if this is too general, though, and I can give you more information about the specific problem. Any references would be helpful, even if you don't have a complete answer!
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What are $a$ and $b$? I don't know if algebraic topology is the best tag for your question. Have you thought of maybe adding some others? – Tyrone Oct 20 '20 at 18:01