Conjugacy, roots, and centralizers in Thompson's group $F$

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We complete the program begun by Brin and Squier of characterising conjugacy in Thompson's group $F$ using the standard action of $F$ as a group of piecewise linear homeomorphisms of the unit interval.
11 pages. The exposition has been rewritten. We have added an extra section which analyses the structure of roots and centralizers; the title has been changed to reflect this. The paper has been submitted for publication

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