Lifts of pseudo-Anosov homeomorphisms of nonorientable surfaces have vanishing SAF invariant

Abstract

We show that any pseudo-Anosov map that is a lift of pseudo-Anosov homeomorphism of a nonorientable surface has vanishing SAF invariant. We also provide a criterion to certify that a pseudo-Anosov map is not such a lift.

arXiv commentRevised according to the referee's suggestions. The most notable addition is the description of the Arnoux-Yoccoz pseudo-Anosovs on nonorientable surfaces and their connection to their lifts to orientable surfaces