# On the Floer homology of plumbed three-manifolds

@article{Ozsvath2003OnTF, title={On the Floer homology of plumbed three-manifolds}, author={Peter S. Ozsvath and Zolt{\'a}n Imre Szab{\'o}}, journal={Geometry \& Topology}, year={2003}, volume={7}, pages={185-224} }

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. These calculations can be used to determine also these groups for other three-manifolds, including the product of a circle with a genus two surface.

## 208 Citations

INVOLUTIVE HEEGAARD FLOER HOMOLOGY AND PLUMBED THREE-MANIFOLDS

- MathematicsJournal of the Institute of Mathematics of Jussieu
- 2017

We compute the involutive Heegaard Floer homology of the family of three-manifolds obtained by plumbings along almost-rational graphs. (This includes all Seifert fibered homology spheres.) We also…

Heegaard Floer homology of some Mazur type manifolds

- Mathematics
- 2012

We show that an infinite family of contractible 4-manifolds have the same boundary as a special type of plumbing. Consequently their Ozsvath--Szabo invariants can be calculated algorithmically. We…

On homology cobordism and local equivalence between plumbed manifolds

- MathematicsGeometry & Topology
- 2019

We establish a structural understanding of the involutive Heegaard Floer homology for all linear combinations of almost-rational (AR) plumbed three-manifolds. We use this to show that the…

Bordered Heegaard Floer Homology and Graph Manifolds

- Mathematics
- 2013

We perform two explicit computations of bordered Heegaard Floer invariants. The first is the type D trimodule associated to the trivial S^1 bundle over the pair of pants P. The second is a bimodule…

Connected Heegaard Floer homology of sums of Seifert fibrations

- MathematicsAlgebraic & Geometric Topology
- 2019

We compute the connected Heegaard Floer homology (defined by Hendricks, Hom, and Lidman) for a large class of 3-manifolds, including all linear combinations of Seifert fibered homology spheres. We…

Heegaard Diagrams and Holomorphic Disks

- Mathematics
- 2004

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…

Surgery obstructions and Heegaard Floer homology

- Mathematics
- 2014

Using Taubes' periodic ends theorem, Auckly gave examples of toroidal and hyperbolic irreducible integer homology spheres which are not surgery on a knot in the three-sphere. We give an obstruction…

Seifert fibered homology spheres with trivial Heegaard Floer homology

- Mathematics
- 2009

We show that among Seifert fibered integer homology spheres, Poincare sphere (with either orientation) is the only non-trivial example which has trivial Heegaard Floer homology. Together with an…

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