${\mathbb{Z}}_2$-Thurston norm in Sol manifolds and embeddability of non-orientable surfaces

Xiaoming Du, Weibiao Wang

For every Sol manifold $M$, we determine the ${\mathbb{Z}}_2$-Thurston norm of every element in $H_2(M;{\mathbb{Z}}_2)$. Each Sol manifold is either a torus bundle over the circle or a…