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2020 Naturality of the contact invariant in monopole Floer homology under strong symplectic cobordisms
Mariano Echeverria
Algebr. Geom. Topol. 20(4): 1795-1875 (2020). DOI: 10.2140/agt.2020.20.1795

Abstract

The contact invariant is an element in the monopole Floer homology groups of an oriented closed three-manifold canonically associated to a given contact structure. A nonvanishing contact invariant implies that the original contact structure is tight, so understanding its behavior under symplectic cobordisms is of interest if one wants to further exploit this property.

By extending the gluing argument of Mrowka and Rollin to the case of a manifold with a cylindrical end, we will show that the contact invariant behaves naturally under a strong symplectic cobordism.

As quick applications of the naturality property, we give alternative proofs for the vanishing of the contact invariant in the case of an overtwisted contact structure, its nonvanishing in the case of strongly fillable contact structures and its vanishing in the reduced part of the monopole Floer homology group in the case of a planar contact structure. We also prove that a strong filling of a contact manifold which is an L–space must be negative definite.

Citation

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Mariano Echeverria. "Naturality of the contact invariant in monopole Floer homology under strong symplectic cobordisms." Algebr. Geom. Topol. 20 (4) 1795 - 1875, 2020. https://doi.org/10.2140/agt.2020.20.1795

Information

Received: 7 September 2018; Revised: 11 August 2019; Accepted: 31 August 2019; Published: 2020
First available in Project Euclid: 1 August 2020

zbMATH: 07226706
MathSciNet: MR4127085
Digital Object Identifier: 10.2140/agt.2020.20.1795

Subjects:
Primary: 57R17, 57R58

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.20 • No. 4 • 2020
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