2017/08/10 by Joshua M. Sabloff, Sabloff, Joshua M., Lisa Traynor +1
Mathematics · #53D12 #FOS: Mathematics #Symplectic Geometry (math.SG) #math.SG #msc:53D12
paper · pdf · doi:10.48550/arxiv.1708.03356
27 pages, 2 figures. v2: References improved. v3: Combined old Theorems 1.1 and 1.2 into a more general Theorem 1.1. Improved statements of several other results in Section 1.3. Smoothed out discussion and corrected errors in the proof of Theorem 1.1 in Sections 5-7, though the overall shape of the proofs has not changed
arxiv created 2018/11/27 · arxiv updated 2018/11/28
We obtain upper and lower bounds for the relative Gromov width of Lagrangian cobordisms between Legendrian submanifolds. Upper bounds arise from the existence of J-holomorphic disks with boundary on the Lagrangian cobordism that pass through the center of any given symplectically embedded ball. The areas of these disks --- and hence the sizes of these balls --- are controlled by a real-valued fundamental capacity, a quantity derived from the algebraic structure of filtered linearized Legendrian Contact Homology of the Legendrian at the top of the cobordism. Lower bounds come from explicit constructions that use neighborhoods of Reeb chords in the Legendrian ends. We also study relationships between the relative Gromov width and another quantitative measurement, the length of a Lagrangian cobordism.