The twisted Floer homology of torus bundles

Abstract

We prove an exact sequence for $\omega$–twisted Heegaard Floer homology. As a corollary, given a torus bundle $Y$ over the circle and a cohomology class $\left[\omega \right]\in H^2\left(Y;\mathbb{Z}\right)$ which evaluates nontrivially on the fiber, we compute the Heegaard Floer homology of $Y$ with twisted coefficients in the universal Novikov ring.