Floer cohomology of lagrangian intersections and pseudo‐holomorphic disks I

Lagrangian non-intersections

“…This extension of Floer's work was developed by Oh [31]. In section 5.2 we describe a spectral sequence which converges to the Floer homology of a Lagrangian.…”

“…The first one is Floer theory for Lagrangian submanifolds. In particular we use the extension of Floer homology to monotone Lagrangian submanifolds due to Oh [31,33,32] which gives rise to an an algebraic approach for computing Floer homology in terms of a spectral sequence. The second ingredient is a geometric technique, developed by the author in [5] and in this paper, by which it is sometimes possible to compute Floer homology in a geometric way.…”

Cluster homology: An overview of the construction and results

“…There are two reasons that make these boundary components disappear; one is purely algebraic and is a cancellation resulting from our graded commutative setting, and the other is analytic and consists in the fact that (as remarked by Oh [12]) the usual gluing argument applies (under generic conditions) to a J-disk passing (transversally) through a and to a itself viewed as a constant strip.…”

Displacement of polydisks and Lagrangian Floer theory

“…Thus the new result is the case that S > 1/2. The proof of this theorem is 'elementary' in that it uses only the Lagrangian Floer theory for monotone Lagrangian submanifolds [10] and by now standard computations for the energy estimates used as in [1], [12], but does not use any techniques of virtual fundamental chains, Bott-Morse theory or any higher homological algebra.…”