# Legendrian satellites and decomposable cobordisms

@article{Guadagni2021LegendrianSA,
title={Legendrian satellites and decomposable cobordisms},
author={Roberta Guadagni and Joshua M. Sabloff and Matthew Yacavone},
journal={Journal of Knot Theory and Its Ramifications},
year={2021}
}
• Published 4 March 2021
• Mathematics
• Journal of Knot Theory and Its Ramifications
. We investigate the interactions between the Legendrian satellite construction and the existence of exact, orientable Lagrangian cobordisms between Legendrian knots. Given Lagrangian cobordisms between two Legendrian knots and between two Legendrian tangles, we construct a Lagrangian cobordism between Legendrian satellites of the knots by the closures of the tangles, with extra twists on both the top and the bottom satellite to compensate for the genus of the cobordism. If the original…
1 Citations

## Figures from this paper

• Mathematics
Association for Women in Mathematics Series
• 2021
Lagrangian cobordisms between Legendrian knots arise in Symplectic Field Theory and impose an interesting and not well-understood relation on Legendrian knots. There are some known “elementary”

## References

SHOWING 1-10 OF 26 REFERENCES

• Mathematics
Association for Women in Mathematics Series
• 2021
Lagrangian cobordisms between Legendrian knots arise in Symplectic Field Theory and impose an interesting and not well-understood relation on Legendrian knots. There are some known “elementary”
• Mathematics
• 2016
In this paper we study Legendrian knots in the knot types of satellite knots. In particular, we classify Legendrian Whitehead patterns and learn a great deal about Legendrian braided patterns. We
We examine the Legendrian analogue of the topological satellite construction for knots, and deduce some results for specific Legendrian knots and links in standard contact three-space and the solid
We provide in this note two relevant examples of Lagrangian cobordisms. The first one gives an example of two exact Lagrangian submanifolds which cannot be composed in an exact fashion. The second
• Mathematics
Journal of Symplectic Geometry
• 2020
We obtain upper and lower bounds for the relative Gromov width of Lagrangian cobordisms between Legendrian submanifolds. Upper bounds arise from the existence of $J$-holomorphic disks with boundary
• Mathematics
• 2013
This paper explores the relationship between the existence of an exact embedded Lagrangian filling for a Legendrian knot in the standard contact $\rr^3$ and the hierarchy of positive, strongly
• Mathematics
Journal of Differential Geometry
• 2020
In this article we define intersection Floer homology for exact Lagrangian cobordisms between Legendrian submanifolds in the contactisation of a Liouville manifold, provided that the
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, we
• Mathematics
• 2015
Embedded Lagrangian cobordisms between Legendrian submanifolds are produced by isotopy, spinning, and handle-attachment constructions that employ the technique of generating families. Moreover, any
• Mathematics
• 2004
Differential graded algebra invariants are constructed for Legendrian links in the 1-jet space of the circle. In parallel to the theory for R 3 , Poincare-Chekanov polynomials and characteristic al-