Some cute applications of Lagrangian cobordisms towards examples in quantitative symplectic geometry

We provide some constructions using Lagrangian cobordisms which improve known examples for some symplectic squeezing problems. Additionally, we prove a flexibility result that Lagrangian submanifolds which are Lagrangian isotopic are also Lagrangian cobordant.

[1]  Ivan Smith,et al.  Quantitative Heegaard Floer cohomology and the Calabi invariant , 2021, Forum of Mathematics, Pi.

[2]  J. Evans A Lagrangian Klein bottle you can’t squeeze , 2020, Journal of Fixed Point Theory and Applications.

[3]  Ely Kerman,et al.  Packing Lagrangian tori , 2021, 2109.01772.

[4]  Jeff Hicks,et al.  Lagrangian cobordisms and Lagrangian surgery , 2021, 2102.10197.

[5]  I. Smith,et al.  Non-displaceable Lagrangian links in four-manifolds , 2019, Geometric and Functional Analysis.

[6]  G. Mikhalkin Examples of tropical-to-Lagrangian correspondence , 2018, European Journal of Mathematics.

[7]  O. Cornea,et al.  Lagrangian cobordism and metric invariants , 2015, Journal of Differential Geometry.

[8]  Weiwei Wu,et al.  Dehn twist exact sequences through Lagrangian cobordism , 2015, Compositio Mathematica.

[9]  Luis Haug Lagrangian antisurgery , 2015, 1511.05052.

[10]  D. Mcduff Displacing Lagrangian toric fibers via probes , 2009, 0904.1686.

[11]  L. Polterovich The Geometry of the Group of Symplectic Diffeomorphism , 2001 .

[12]  V. I. Arnol’d Lagrange and legendre cobordisms. I , 1980 .