Corpus ID: 235390828

# Reeb chords of Lagrangian slices

@inproceedings{Chantraine2021ReebCO,
title={Reeb chords of Lagrangian slices},
author={Baptiste Chantraine},
year={2021}
}
In this short note we observe that the boundary of a properly embedded compact exact Lagrangian sub-manifold in a subcritical Weinstein domain X necessarily admits Reeb chords. The existence of a Reeb chord either follows from an obstruction to the deformation of the boundary to a cylinder over a Legendrian sub-manifold or from the fact that the wrapped Floer homology of the Lagrangian vanishes once this boundary has been “collared”.

#### References

SHOWING 1-10 OF 22 REFERENCES
Some non-collarable slices of Lagrangian surfaces
In this note we define the notion of collarable slices of Lagrangian submanifolds. Those are slices of Lagrangian submanifolds which can be isotoped through Lagrangian submanifolds to a cylinder overExpand
Lagrangian caps
• Mathematics
• 2013
We establish an h-principle for exact Lagrangian embeddings with concave Legendrian boundary. We prove, in particular, that in the complement of the unit ball B in the standard symplecticExpand
Lagrangian concordance of Legendrian knots
In this article, we define the notion of a Lagrangian concordance between two Legendrian knots analogous to smooth concordance in the Legendrian context. We show that Legendrian isotopic LegendrianExpand
Exact Lagrangian caps of Legendrian knots
We prove that any Legendrian knot in $(S^3,\xi_{std})$ bounds an exact Lagrangian surface in $\mathbb{R}^4\setminus B^4$ after a sufficient number of stabilizations. In order to show this, weExpand
Floer theory for Lagrangian cobordisms
• Mathematics
• 2015
In this article we define intersection Floer homology for exact Lagrangian cobordisms between Legendrian submanifolds in the contactisation of a Liouville manifold, provided that theExpand
An open string analogue of Viterbo functoriality
• Mathematics
• 2007
In this preprint, we look at exact Lagrangian submanifolds with Legendrian boundary inside a Liouville domain. The analogue of symplectic cohomology for such submanifolds is called “wrapped FloerExpand
First steps in symplectic topology
CONTENTSIntroduction § 1. Is there such a thing as symplectic topology? § 2. Generalizations of the geometric theorem of Poincare § 3. Hyperbolic Morse theory § 4. Intersections of LagrangianExpand
Proof of the Arnold chord conjecture in three dimensions, II
• Mathematics
• 2013
In "Proof of the Arnold chord conjecture in three dimensions I", we deduced the Arnold chord conjecture in three dimensions from another result, which asserts that an exact symplectic cobordismExpand
Obstructions to Lagrangian concordance
• Mathematics
• 2014
We investigate the question of the existence of a Lagrangian concordance between two Legendrian knots in $\mathbb{R}^3$. In particular, we give obstructions to a concordance from an arbitrary knot toExpand
On homological rigidity and flexibility of exact Lagrangian endocobordisms
• Mathematics
• 2014
We show that an exact Lagrangian cobordism L ⊂ ℝ × P × ℝ from a Legendrian submanifold Λ ⊂ P × ℝ to itself satisfies Hi(L; 𝔽) = Hi(Λ; 𝔽) for any field 𝔽, given that Λ admits a spin exactExpand