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

We show that any pseudo-Anosov map that is a lift of a 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.

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The paper was written while the author was a member at the Institute for Advanced Study. The author thanks the IAS for its hospitality. He also thanks the referee for many thoughtful remarks and Livio Liechti for helpful comments on an earlier version of this paper.

This work was supported by NSF grant DMS-1128155.

Received 11 May 2016

Accepted 16 January 2017

Published 5 July 2018