Mathematics

Translation surfaces can be viewed as polygons with parallel and equal sides
identified. A homeomorphism on a translation surface to itself is called pseudo-
Anosov when its derivative is a constant matrix in SL(2,R) whose trace is larger
than 2. We apply Veech's construction of pseudo-Anosov homeomorphisms to
produce infinite families of pseudo-Anosov maps in the stratum H(2,2) with vanishing
Sah-Arnoux-Fathi invariant, as well as sporadic examples in other strata.