# Algebraic torsion via Heegaard Floer homology

@article{Kutluhan2015AlgebraicTV, title={Algebraic torsion via Heegaard Floer homology}, author={Çağatay Kutluhan and Gordana Mati{\'c} and Jeremy van Horn-Morris and Andy Wand}, journal={arXiv: Symplectic Geometry}, year={2015} }

We outline Hutchings's prescription that produces an ECH analog of Latschev and Wendl's algebraic $k$-torsion in the context of $ech$, a variant of ECH used in a proof of the isomorphism between Heegaard Floer and Seiberg-Witten Floer homologies; and we explain how it translates into Heegaard Floer homology.

## 7 Citations

Algebraic and Giroux torsion in higher-dimensional contact manifolds

- Mathematics
- 2019

We construct examples in any odd dimension of contact manifolds with finite and non-zero algebraic torsion (in the sense of Latschev-Wendl), which are therefore tight and do not admit strong…

Filtering the Heegaard Floer contact invariant

- Mathematics
- 2016

We define an invariant of contact structures in dimension three from Heegaard Floer homology. This invariant takes values in the set $\mathbb{Z}_{\geq0}\cup\{\infty\}$. It is zero for overtwisted…

Algebraic torsion for contact manifolds with convex boundary

- Mathematics
- 2016

We extend the Heegaard Floer homological definition of algebraic torsion (AT) for closed contact 3-manifolds due to Kutluhan et al. to contact 3-manifolds with convex boundary. We show that the AT of…

SFT COMPUTATIONS AND INTERSECTION THEORY IN HIGHER-DIMENSIONAL CONTACT MANIFOLDS

- MathematicsJournal of the Institute of Mathematics of Jussieu
- 2021

Abstract I construct infinitely many nondiffeomorphic examples of
$5$
-dimensional contact manifolds which are tight, admit no strong fillings and do not have Giroux torsion. I obtain obstruction…

Algebraic Torsion in Higher-Dimensional Contact Manifolds

- Mathematics
- 2019

We construct examples in any odd dimension of contact manifolds with finite and non-zero algebraic torsion (in the sense of Latschev-Wendl), which are therefore tight and do not admit strong…

Properties and applications of the annular filtration on Khovanov homology

- Mathematics
- 2016

The first part of this thesis is on properties of annular Khovanov homology. We prove a connection between the Euler characteristic of annular Khovanov homology and the classical Burau representation…

Spectral order for contact manifolds with convex boundary

- MathematicsAlgebraic & Geometric Topology
- 2018

We extend the Heegaard Floer homological definition of spectral order for closed contact 3-manifolds due to Kutluhan, Matic, Van Horn-Morris, and Wand to contact 3-manifolds with convex boundary. We…

## References

SHOWING 1-10 OF 22 REFERENCES

LECTURES ON THE EQUIVALENCE OF HEEGAARD FLOER AND SEIBERG–WITTEN FLOER HOMOLOGIES

- Mathematics
- 2013

This article gives a detailed account of the lectures delivered by the author on the construction, in joint work with Yi-Jen Lee and Clifford H. Taubes, of isomorphisms between Heegaard Floer and…

HF=HM, I : Heegaard Floer homology and
Seiberg–Witten Floer homology

- MathematicsGeometry & Topology
- 2020

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…

On the contact class in Heegaard Floer homology

- Mathematics
- 2006

We present an alternate description of the Ozsvath-Szabo contact class in Heegaard Floer homology. Using our contact class, we prove that if a contact structure (M,\xi) has an adapted open book…

A cylindrical reformulation of Heegaard Floer homology

- Mathematics
- 2006

We reformulate Heegaard Floer homology in terms of holomorphic curves in the cylindrical manifold U a0;1c R, where U is the Heegaard surface, instead of Sym g .U/. We then show that the entire…

HF=HM, III : Holomorphic curves and the
differential for the ech/Heegaard Floer correspondence

- MathematicsGeometry & Topology
- 2020

This is the third of five papers that construct an isomorphism between the Seiberg-Witten Floer homology and the Heegaard Floer homology of a given compact, oriented 3-manifold. The isomorphism is…

HF=HM, II : Reeb orbits and holomorphic
curves for the ech/Heegaard Floer correspondence

- MathematicsGeometry & Topology
- 2020

This is the second of five papers that construct an isomorphism between the Seiberg-Witten Floer homology and the Heegaard Floer homology of a given compact, oriented 3-manifold. The isomorphism is…

Filtering the Heegaard Floer contact invariant

- Mathematics
- 2016

We define an invariant of contact structures in dimension three from Heegaard Floer homology. This invariant takes values in the set $\mathbb{Z}_{\geq0}\cup\{\infty\}$. It is zero for overtwisted…

A combinatorial description of the Heegaard Floer contact invariant

- Mathematics
- 2007

We observe that the Heegaard Floer contact invariant is combinatorial by applying the algorithm of Sarkar-Wang to the description of the contact invariant due to Honda-Kazez-Matic. We include an…

Correction to the article: A cylindrical reformulation of Heegaard Floer homology

- Mathematics
- 2014

This note corrects one serious mistake and several smaller mistakes from arXiv:math/0502404. The main results of that paper are unchanged.