In this article, we prove that the centralizer C of the cyclic subgroup Z of a surface mapping class group generated by a pseudo-Anosov mapping class A is a finite extension of an infinite cyclic group. In addition, we prove that the normalizer of Z is either equal to C or contains C as a normal subgroup of index 2.
Note: This paper was originally written on March 5, 1982. The bibliography has been updated and minor changes have been made in the text to clarify the original arguments.
Contact: mccarthy@math.msu.edu Last Revised 9/2/99