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Mather invariant in groups of piecewise-linear homeomorphisms

Matucci, Francesco

Trends in Mathematics, Combinatorial and Geometric Group Theory, (2010), 251-260 (preprint -

We describe the relation between two characterizations of conjugacy in groups of piecewise-linear homeomorphisms, discovered by Brin and Squier in [2] and Kassabov and Matucci in [5]. Thanks to the interplay between the techniques, we produce a simplified point of view of conjugacy that allows us to easily recover centralizers and lends itself to generalization.