A construction of pseudo-Anosov homeomorphisms using positive twists

Abstract

We introduce a construction of pseudo-Anosov homeomorphisms on n-times punctured spheres and surfaces of higher genus using only positive half-twists and Dehn twists. These constructions produce explicit examples of pseudo-Anosov maps with various number-theoretic properties associated to the stretch factors. For instance, we produce examples where the trace field is not totally real and the Galois conjugates of the stretch factor are on the unit circle. It follows that for these examples, no power of these maps can arise from either Thurston's or Penner's constructions.