Lagrangian Floer theory on compact toric manifolds II: bulk deformations

By K. Fukaya, Yong-Geun Oh, H. Ohta, K. Ôno. 2008

297 citations recorded by the source corpus.

This is a continuation of part I in the series of the papers on Lagrangian Floer theory on toric manifolds. Using the deformations of Floer cohomology by the ambient cycles, which we call bulk deformations, we find a continuum of non-displaceable Lagrangian fibers on some compact toric manifolds. We also provide a method of finding all fibers with non-vanishing Floer cohomology with bulk deformations in arbitrary compact toric manifolds, which we call bulk-balanced Lagrangian fibers.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4633dac49a92f0c9d843c3a6ea2aec14b29a879a

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Citations in the corpus

Fukaya A∞-structures Associated to Lefschetz Fibrations. II (2014, background): “wider class of deformations with the same formal behaviour (our \B-elds" are more general than the standard terminology, and can be viewed as a special case of \bulk terms" in the sense of [17]; that paper demonstrates the usefulness of this additional exibility). Question 1.1. Can we choo”
Toric degenerations of Gelfand-Cetlin systems and potential functions (2008, methodology): “In Section 12, we prove the existence of a non-displaceable Lagrangian torus in the flag manifold along the lines of [9].”
Deformed Hamiltonian Floer theory, capacity estimates and Calabi quasimorphisms (2010, methodology): “Oh, and K. Ono for telling me about their related (and independent) joint work with Ohta [FOOO11], and L. Polterovich for interesting comments.”
The structure of 2D semi-simple field theories (2007, result): “, as well as blow-ups of such varieties at any number of points [B]. Of these,only for toric ones does the open-closedtheory seem to be in convincing shape, thanks to work by Fukaya and collaborators [FOOO]. Acknowledgements I have lectured on successive approximations of this work since the fall of”
Counting pseudo-holomorphic discs in Calabi-Yau 3 fold (2009, background): “here numerical invariant is deﬁned is the case when M is a toric manifold and L is its Tn orbit. In that case Mℓ,k(L;β;J) of β ∈ H2(M,L;Z) with Maslov index ≥ 2 only is related to our structures. See [9] and references therein for this case. 8.3. The case of real point. We assume dimCM = 3 and let τ”
On the Fukaya category of a Fano hypersurface in projective space (2013, background): “ve an embedding of Cninto Mc weak(L), such that the resulting disc potential is given by W. This is a partial analogue of the result proven in the case of toric varieties by Cho and Oh [15] (see also [27, 28, 24]): the mirror is equal to the Maurer–Cartan moduli space, with the superpotential given ”
Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces (2012, methodology): “(Thus, local systems are conceptually an exponentiated variant of the “bounding cochains” used by Fukaya et al [15, 16]).”
Gauged Floer Theory Of Toric Moment Fibers (2010, methodology): “s displaceable then HF(L,φ(L)) vanishes. On the other hand, one can sometimes compute HF(L,φ(L)) by, for example, taking φsmall and identifying it with the Morse homology. In a series of papers [21], [19] Fukaya-Oh-Ohta-Ono used this strategy to prove non-displaceability results for certain moment ﬁ”
Floer cohomology and pencils of quadrics (2010, unknown): “According to the theory of [34], cf.”
Cyclic symmetry and adic convergence in Lagrangian Floer theory (2009, unknown): “The notion of continuous family of multisections had already been used in [12] Section 33, [7],[15] etc.”
The monotone wrapped Fukaya category and the open-closed string map (2012, methodology): “We assume the reader has some familiarity with the relevant literature (Cho-Oh [17], Auroux [12], Fukaya-Oh-OhtaOno [22]), and we refer to [36, Appendix] for details.”