For a Legendrian link with or , immersed exact Lagrangian fillings of can be lifted to conical Legendrian fillings of . When is embedded, using the version of functoriality for Legendrian contact homology (LCH) from Pan and Rutherford [J. Symplectic Geom.
Constructions of Lagrangian cobordisms
Lagrangian cobordisms between Legendrian knots arise in Symplectic Field Theory and impose an interesting and not wellunderstood relation on Legendrian knots. There are some known ``elementary'' building blocks for Lagrangian cobordisms that are smoothly the attachment of 0 and 1handles. An important question is whether every pair of nonempty 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.
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 Award ID(s):
 1703356
 NSFPAR ID:
 10298497
 Editor(s):
 Acu, Bahar; Cannizzo, Catherine; McDuff, Dusa; Myer, Ziva; Pan, Yu; Traynor, Lisa
 Date Published:
 Journal Name:
 Association for Women in Mathematics series
 Volume:
 27
 ISSN:
 23645733
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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