Abstract / Description of output
Lagrangian k-surgery modifies an immersed Lagrangian submanifold by topological k-surgery while removing a self-intersection. Associated to a k-surgery is a Lagrangian surgery trace cobordism. We prove that every Lagrangian cobordism is exactly homotopic to a concatenation of suspension cobordisms and Lagrangian surgery traces. This exact homotopy can be chosen with as small Hofer norm as desired. Furthermore, we show that each Lagrangian surgery trace bounds a holomorphic teardrop pairing the Morse cochain associated with the handle attachment to the Floer cochain generated by the self-intersection. We give a sample computation for how these decompositions can be used to algorithmically construct bounding cochains for Lagrangian submanifolds. In an appendix, we describe a 2-ended embedded monotone Lagrangian cobordism which is not the suspension of a Hamiltonian isotopy following a suggestion of Abouzaid and Auroux.
Original language | English |
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Pages (from-to) | 509-595 |
Journal | Commentarii Mathematici Helvetici: A Journal of the Swiss Mathematical Society (CMH) |
Volume | 98 |
Issue number | 3 |
DOIs | |
Publication status | Published - 4 Nov 2023 |