Can I read Obstructions to reversing Lagrangian surgery in Lagrangian fillings on EtoBox?

Obstructions to reversing Lagrangian surgery in Lagrangian fillings by Capovilla-Searle, Orsola; Legout, Noémie; Limouzineau, Maÿlis; Murphy, Emmy; Pan, Yu; Traynor, Lisa is a scholarly article available to read on EtoBox.

What is Obstructions to reversing Lagrangian surgery in Lagrangian fillings about?

Given an immersed, Maslov-$0$, exact Lagrangian filling of a Legendrian knot, if the filling has a vanishing index and action double point, then through Lagrangian surgery it is possible to obtain a new immersed, Maslov-$0$, exact Lagrangian filling with one less double point and with genus increased by one. We show that it is not always possible to reverse the Lagrangian surgery: not every immersed, Maslov-$0$, exact Lagrangian filling with genus $g \geq 1$ and $p$ double points can be obtained from such a Lagrangian surgery on a filling of genus $g-1$ with $p+1$ double points. To show this, we establish the connection between the existence of an immersed, Maslov-$0$, exact Lagrangian filling of a Legendrian $\Lambda$ that has $p$ double points with action $0$ and the existence of an embedded, Maslov-$0$, exact Lagrangian cobordism from $p$ copies of a Hopf link to $\Lambda$. We then prove that a count of augmentations provides an obstruction to the existence of embedded, Maslov-$0$, exact Lagrangian cobordisms between Legendrian links.

Author

Capovilla-Searle, Orsola; Legout, Noémie; Limouzineau, Maÿlis; Murphy, Emmy; Pan, Yu; Traynor, Lisa

Published

2022

Language

EN