Georgia Institute of Technology College of Sciences

Construction of pseudo-Anosov elements of mapping class groups of surfaces is a non-trivial task. In 1988, Penner gave a very general construction of pseudo-Anosov mapping classes, and he conjectured that all pseudo-Anosov mapping classes arise this way up to finite power. This conjecture was known to be true on some simple surfaces, including the torus. In joint work with Hyunshik Shin, we resolve this conjecture for all surfaces.