# Legendrian Satellites and Decomposable Cobordisms

@inproceedings{Guadagni2021LegendrianSA, title={Legendrian Satellites and Decomposable Cobordisms}, author={Roberta Guadagni and Joshua M. Sabloff and Matthew Yacavone}, year={2021} }

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… Expand

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#### References

SHOWING 1-10 OF 33 REFERENCES

Constructions of Lagrangian cobordisms

- Mathematics
- 2020

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”… Expand

Legendrian satellites

- 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… Expand

The Legendrian Satellite Construction

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… Expand

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 the… Expand

A note on exact Lagrangian cobordisms with disconnected Legendrian ends

- Mathematics
- 2013

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… Expand

The relative Gromov width of Lagrangian cobordisms between Legendrians

- Mathematics
- 2017

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… Expand

Positive knots and Lagrangian fillability

- 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… Expand

Lagrangian cobordisms via generating families: Construction and geography

- 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… Expand

Exact Lagrangian caps of Legendrian knots

- Mathematics
- 2013

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… Expand

Legendrian solid-torus links

- 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-… Expand