Correction terms, ${\mathbb{Z}}_2$--Thurston norm, and triangulations

We show that the correction terms in Heegaard Floer homology give a lower bound to the the genus of one-sided Heegaard splittings and the $\mathbb Z_2$–Thurston norm. Using a result of Jaco–Rubinstein–Tillmann, this gives a lower bound to the complexity of certain closed $3$–manifolds. As an application, we compute the ${\mathbb{Z}}_2$–Thurston norm of the double branched cover of some closed 3–braids, and give upper and lower bounds for the complexity of these manifolds.