Lagrangian embeddings and Lagrangian cobordism

1997 ◽  
pp. 13-23 ◽  
Author(s):  
Yu. V. Chekanov
Keyword(s):  
Lagrangian Cobordism

scholarly journals In simply connected cotangent bundles, exact Lagrangian cobordisms are h-cobordisms

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Hiro Lee Tanaka
Keyword(s):  
Connected Manifold ◽  
Cotangent Bundles ◽  
Lagrangian Cobordisms ◽  
Simply Connected ◽  
Lagrangian Cobordism

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.

scholarly journals Lagrangian cobordism and metric invariants

2019 ◽  
Vol 112 (1) ◽  
pp. 1-45
Author(s):  
Octav Cornea ◽  
Egor Shelukhin
Keyword(s):  
Metric Invariants ◽  
Lagrangian Cobordism

scholarly journals Invariants of Lagrangian cobordisms via spectral numbers

2019 ◽  
Vol 11 (01) ◽  
pp. 205-231 ◽  
Author(s):  
Mads R. Bisgaard
Keyword(s):  
Spectral Invariants ◽  
Lagrangian Cobordisms ◽  
Lagrangian Cobordism

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.

scholarly journals Exact Lagrangian cobordism and pseudo-isotopy

2017 ◽  
Vol 28 (08) ◽  
pp. 1750059 ◽  
Author(s):  
Lara Simone Suárez
Keyword(s):  
Dimension Formula ◽  
Lagrangian Cobordism

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.

scholarly journals The minimal length of a Lagrangian cobordism between Legendrians

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

scholarly journals Lagrangian cobordism and Fukaya categories

2014 ◽  
Vol 24 (6) ◽  
pp. 1731-1830 ◽  
Author(s):  
Paul Biran ◽  
Octav Cornea
Keyword(s):  
Fukaya Categories ◽  
Lagrangian Cobordism

scholarly journals The fundamental group of a rigid Lagrangian cobordism

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

scholarly journals Genus One Cobordisms Between Torus Knots

2020 ◽  
Author(s):  
Peter Feller ◽  
JungHwan Park
Keyword(s):  
Torus Knots ◽  
Explicit Constructions ◽  
Single Crossing ◽  
Heegaard Floer ◽  
Genus One ◽  
Lagrangian Cobordism

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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