Conjugacy Classes of the Piecewise Linear Group Conjugacy Classes of the Piecewise Linear Group

by Housley, Matthew L

The piecewise linear group is the set of all piecewise linear orientation preserving homeomorphisms from the interval to itself under the operation of composition. We present here a complete set of invariants to classify the conjugacy classes of this group. Our approach to this problem relies on the factorization of elements into elements having only a single breakpoint.