Lagrangian embeddings and Lagrangian cobordism

Author(s):  
Yu. V. Chekanov
Keyword(s):  
2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Hiro Lee Tanaka

Abstract Let Q be a simply connected manifold. We show that every exact Lagrangian cobordism between compact, exact Lagrangians in T*Q is an h-cobordism. This is a corollary of the Abouzaid–Kragh Theorem.


2019 ◽  
Vol 112 (1) ◽  
pp. 1-45
Author(s):  
Octav Cornea ◽  
Egor Shelukhin

2019 ◽  
Vol 11 (01) ◽  
pp. 205-231 ◽  
Author(s):  
Mads R. Bisgaard

We extend parts of the Lagrangian spectral invariants package recently developed by Leclercq and Zapolsky to the theory of Lagrangian cobordism developed by Biran and Cornea. This yields a nondegenerate Lagrangian “spectral metric” which bounds the Lagrangian “cobordism metric” (recently introduced by Cornea and Shelukhin) from below. It also yields a new numerical Lagrangian cobordism invariant as well as new ways of computing certain asymptotic Lagrangian spectral invariants explicitly.


2017 ◽  
Vol 28 (08) ◽  
pp. 1750059 ◽  
Author(s):  
Lara Simone Suárez

We show that under some topological assumptions, an exact Lagrangian cobordism [Formula: see text] of dimension [Formula: see text] is a Lagrangian pseudo-isotopy. This result is a weaker form of a conjecture proposed by Biran and Cornea, which states that any exact Lagrangian cobordism is Hamiltonian isotopic to a Lagrangian suspension.


2016 ◽  
Vol 23 (2) ◽  
pp. 1419-1448 ◽  
Author(s):  
Joshua M. Sabloff ◽  
Lisa Traynor

2014 ◽  
Vol 24 (6) ◽  
pp. 1731-1830 ◽  
Author(s):  
Paul Biran ◽  
Octav Cornea

2018 ◽  
Vol 43 (1) ◽  
pp. 125-144
Author(s):  
Jean-François Barraud ◽  
Lara Simone Suárez

Author(s):  
Peter Feller ◽  
JungHwan Park

Abstract We determine the pairs of torus knots that have a genus one cobordism between them, with one notable exception. This is done by combining obstructions using $\nu ^+$ from the Heegaard Floer knot complex and explicit constructions of cobordisms. As an application, we determine the pairs of torus knots related by a single crossing change. Also, we determine the pairs of Thurston–Bennequin number maximizing Legendrian torus knots that have a genus one exact Lagrangian cobordism, with one exception.


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