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
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- 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…
SFT COMPUTATIONS AND INTERSECTION THEORY IN HIGHER-DIMENSIONAL CONTACT MANIFOLDS
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We construct infinitely many non-diffeomorphic examples of $5$-dimensional contact manifolds which are tight, admit no strong fillings, and do not have Giroux torsion. We obtain obstruction results…
Algebraic torsion for contact manifolds with convex boundary
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- 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…
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
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- 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…
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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…
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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
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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…
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This note corrects one serious mistake and several smaller mistakes from arXiv:math/0502404. The main results of that paper are unchanged.