相关论文: Heegaard Floer homology of mapping tori II

We calculate the Heegaard Floer homologies$HF^+(M,s) for mapping tori M associated to certain surface diffeomorphisms, where s is any Spin^c structure on M whose first Chern class is non-torsion. Let gamma and delta be a pair of…

We make a detailed study of the Heegaard Floer homology of the product of a closed surface Sigma_g of genus g with S^1. We determine HF^+ for this 3-manifold completely for the spin^c structure having trivial first Chern class, which for…

We calculate the Heegaard Floer homologies for three-manifolds obtained by plumbings of spheres specified by certain graphs. Our class of graphs is sufficiently large to describe, for example, all Seifert fibered rational homology spheres.…

We establish a relationship between Heegaard Floer homology and the fractional Dehn twist coefficient of surface automorphisms. Specifically, we show that the rank of the Heegaard Floer homology of a 3-manifold bounds the absolute value of…

For an open book decomposition $(S,\phi)$, the fractional Dehn twist coefficients are rational numbers measuring the amount that the monodromy $\phi$ twists the surface $S$ near each boundary component. In general, the twist coefficients do…

Modifying the method of [21], we compute the perturbed $HF^+$ for some special classes of fibered three manifolds in the second highest spin$^c$-structures $S_{g-2}$. The special classes considered in this paper include the mapping tori of…

Let M be a closed, connected and oriented 3-manifold. This article is the first of a five part series that constructs an isomorphism between the Heegaard Floer homology groups of M and the corresponding Seiberg-Witten Floer homology groups…

We prove that the knot Floer complex of a fibered knot detects whether the monodromy of its fibration is right-veering. In particular, this leads to a purely knot Floer-theoretic characterization of tight contact structures, by the work of…

For an oriented irreducible 3-manifold M with non-empty toroidal boundary, we describe how sutured Floer homology ($SFH$) can be used to determine all fibered classes in $H^1(M)$. Furthermore, we show that the $SFH$ of a balanced sutured…

We show that a rational homology solid torus is a Heegaard Floer homology solid torus if and only if it has a Dehn filling with a non-separating 2-sphere. Using this, we characterize Seifert fibered Heegaard Floer solid tori.

Let K \subset Y be a knot in a three manifold which admits a longitude-framed surgery such that the surgered manifold has first Betti number greater than that of Y. We find a formula which computes the twisted Floer homology of the surgered…

Given a closed 3--manifold $Y$, we show that the Heegaard Floer homology determines whether $Y$ fibres over the circle with a fibre of negative Euler characteristic. This is an analogue of an earlier result about knots proved by Ghiggini…

A three-manifold equipped with a Heegaard diagram can be used to set up a Floer homology theory whose differential counts pseudo-holomorphic disks in the $g$-fold symmetric product of the Heegaard surface. This leads to a topological…

We construct a class of codimension-2 solutions in supergravity that realize T-folds with arbitrary $O(2,2,\mathbb{Z})$ monodromy and we develop a geometric point of view in which the monodromy is identified with a product of Dehn twists of…

In this paper, we write down a special Heegaard diagram for a given product three manifold $\Sigma_g\times S^1$. We use the diagram to compute its perturbed Heegaard Floer homology.

We show that if the monodromy of a 3-manifold M that fibers over the circle has large translation distance in the curve complex, then the rank of the fundamental group of M is 2g+1, where g is the genus of the fiber.

We use Heegaard Floer homology with twisted coefficients to define numerical invariants for arbitrary closed 3-manifolds equipped torsion spin$^c$ structures, generalising the correction terms (or $d$--invariants) defined by Ozsv\'ath and…

Given a Lagrangian submanifold $L$ in a symplectic manifold $X$, the homological Lagrangian monodromy group $\mathcal{H}_L$ describes how Hamiltonian diffeomorphisms of $X$ preserving $L$ setwise act on $H_*(L)$. We begin a systematic study…

Bordered Heegaard Floer homology is an invariant for three-manifolds with boundary. In particular, this invariant associates to a handle decomposition of a surface F a differential graded algebra, and to an arc slide between two handle…

We define a notion of Heegaard Floer homology for three dimensional orbifolds with arbitrary cyclic singularities, generalizing the recent work of Biji Wong where the singular locus is assumed to be connected.