The twisted Floer homology of torus bundles

TL;DR

This paper computes the Heegaard Floer homology with twisted coefficients for torus bundles over the circle, revealing new insights into their topological invariants.

Contribution

It provides explicit calculations of twisted Floer homology for torus bundles, a novel extension of existing Floer theory results.

Findings

Explicit formulas for Floer homology of torus bundles

Demonstrates nontrivial evaluation of cohomology on fibers

Advances understanding of 3-manifold invariants

Abstract

Given a torus bundle $Y$ over the circle and a cohomology class $[\omega]\in H^2(Y;\mathbb{Z})$ which evaluates nontrivially on the fiber, we compute the Heegaard Floer homology of $Y$ with twisted coefficients in the universal Novikov ring.