Correction terms, Z₂--Thurston norm, and triangulations

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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 Z₂--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 Z₂--Thurston norm of the double branched cover of some closed 3--braids, and give upper and lower bounds for the complexity of these manifolds.