## Journal of Symplectic Geometry

### $U$-action on perturbed Heegaard Floer homology

Zhongtao Wu

#### Abstract

This paper has two purposes. First, as a continuation of "Perturbed Floer homology of some fibered three manifolds," we apply a similar method to compute the perturbed $HF^+$ for some special classes of fibered three-manifolds in the second highest $spin^c$-structures, including the mapping tori of Dehn twists along a single non-separating curve and along a transverse pair of curves. Second, we establish an adjunction inequality for the perturbed Heegaard Floer homology, which indicates a potential connection between the $U$-action on the homology group and the Thurston norm of a three-manifold. As an application, we find the $U$-action on the perturbed $HF^+$ of the above classes of fibered three-manifolds is trivial.

#### Article information

Source
J. Symplectic Geom., Volume 10, Number 3 (2012), 423-445.

Dates
First available in Project Euclid: 16 October 2012

Wu, Zhongtao. $U$-action on perturbed Heegaard Floer homology. J. Symplectic Geom. 10 (2012), no. 3, 423--445. https://projecteuclid.org/euclid.jsg/1350392492