Constructions of Lagrangian cobordisms
Abstract
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" building blocks for Lagrangian cobordisms that are smoothly the attachment of - and -handles. An important question is whether every pair of non-empty Legendrians that are related by a connected Lagrangian cobordism can be related by a ribbon Lagrangian cobordism, in particular one that is "decomposable" into a composition of these elementary building blocks. We will describe these and other combinatorial building blocks as well as some geometric methods, involving the theory of satellites, to construct Lagrangian cobordisms. We will then survey some known results, derived through Heegaard Floer Homology and contact surgery, that may provide a pathway to proving the existence of nondecomposable (nonribbon) Lagrangian cobordisms.
Keywords
Cite
@article{arxiv.2101.00031,
title = {Constructions of Lagrangian cobordisms},
author = {Sarah Blackwell and Noémie Legout and Caitlin Leverson and Maÿlis Limouzineau and Ziva Myer and Yu Pan and Samantha Pezzimenti and Lara Simone Suárez and Lisa Traynor},
journal= {arXiv preprint arXiv:2101.00031},
year = {2021}
}
Comments
27 pages, 20 figures. Survey paper submitted to Proceedings of the 2019 Research Collaboration Conference for Women in Symplectic and Contact Geometry and Topology (WiSCon) Workshop