Georgia Institute of Technology College of Sciences

Mapping classes are the natural topological symmetries of surfaces. Their study is often restricted to the orientation-preserving ones, which form a normal subgroup of index two in the group of all mapping classes. In this talk, we discuss orientation-reversing mapping classes. In particular, we show that Lehmer's question from 1933 on Mahler measures of integer polynomials can be reformulated purely in terms of a comparison between orientation-preserving and orientation-reversing mapping classes.