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Title: Constructions of Lagrangian cobordisms
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 0- and 1-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.  more » « less
Award ID(s):
1703356
PAR ID:
10298497
Author(s) / Creator(s):
; ; ; ; ; ; ; ;
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:
2364-5733
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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