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September 2012 $U$-action on perturbed Heegaard Floer homology
Zhongtao Wu
J. Symplectic Geom. 10(3): 423-445 (September 2012).

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.

Citation

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Zhongtao Wu. "$U$-action on perturbed Heegaard Floer homology." J. Symplectic Geom. 10 (3) 423 - 445, September 2012.

Information

Published: September 2012
First available in Project Euclid: 16 October 2012

zbMATH: 1264.53078
MathSciNet: MR2983436

Rights: Copyright © 2012 International Press of Boston

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Vol.10 • No. 3 • September 2012
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