Construction of pseudo-Anosov maps and a conjecture of Penner

Balazs Strenner (Princeton)

Abstract: There are many constructions of pseudo-Anosov elements of mapping class groups of surfaces. Some of them are known to generate all pseudo-Anosov mapping classes, others are known not to. 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, but has otherwise remained open. In this talk I prove that the conjecture is false for most surfaces. (This is joint work with Hyunshik Shin.)