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Under "Applications to growth", the second bullet point is wrong, that inequality does not hold for all w. One exception occurs when w is trivial. There are other exceptions, but they occur only in a very exceptional case, namely when the outer automorphism corresponds to a homeomorphism of a surface with boundary. And even in that case, the exceptions are limited to the situation when w corresponds to a path around a boundary component of the surface. Mosher (talk) 22:26, 10 January 2020 (UTC)[reply]
