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

Abstract

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.

20 pages, 5 figures

References in corpus (1)

• Layered-triangulations of 3-manifolds