Lagrangian intersection floer theory : anomaly and obstruction

By 深谷賢治, Yong-Geun Oh, H. Ohta, K. Ôno. 2009

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Citations in the corpus

Covariantly functorial wrapped Floer theory on Liouville sectors (2017, unknown): “for Liouville sectors, where n = 1 2 dimX (generalizing definitions given by Fukaya–Oh–Ohta– Ono [21], Seidel [44], and Abouzaid [1]) and we show that OC is a natural transformation of functors, meaning it commutes with the pushforward maps induced by inclusions of Liouville sectors (we adopt the co”
Conjectures on Bridgeland stability for Fukaya categories of Calabi-Yau manifolds, special Lagrangians, and Lagrangian mean curvature flow (2014, methodology): “Some references are McDuff and Salamon [52] for symplectic geometry, the author [42] and Harvey and Lawson [27] for Calabi–Yau m-folds and special Lagrangians, Mantegazza [50], Smoczyk [67] and Neves [56] for (Lagrangian) MCF, Fukaya [18, 19], Fukaya, Oh, Ohta and Ono [20] and Seidel [64] for Lagran”
Virtual fundamental classes for moduli spaces of sheaves on Calabi-Yau four-folds (2015, methodology): “Kuranishi neighbourhoods above are essentially the same as those in [16,18,29, 30], omitting finite groups, and our coordinate changes above are a common generalization of the different notions used in [16, 18] and [29, 30].”
Bounds on spectral norms and barcodes (2018, background): “ientable, one expects this statement to hold in full generality, with coecients in a eld of characteristic 0;by techniques of virtual fundamental cycles in Hamiltonian Floer theory (see [47, 70, 88],[45, 54, 55, 56], and see also [57, 73] for a recent description of the state of the art and further ”
The wall-crossing formula and Lagrangian mutations (2017, background): “We note that the potential for the cubic surface was also computed by Fukaya-Oh-Ohta-Ono [18, section 24].”
Fukaya A∞-structures Associated to Lefschetz Fibrations. II (2014, background): “For n6= 2, the existence of such a representative is clear from homological algebra (the objects are spheres, and one can arrange that they have no endomorphisms of degree 2 on the cochain level; see [16] for the general formalism). For n= 2, it follows from basic considerations involving holomorphi”
AN INTRODUCTION TO KNOT FLOER HOMOLOGY (2014, unknown): “pseudo-holomorphic disks in Symd(Σ) with boundaries on Tαand Tβ. This kind of construction was ﬁrst proposed by Floer [Flo88], and then developed by various authors [FHS95], [Oh97a], [Oh96], [Oh97b], [FOOO09a], [FOOO09b]. In our setting, note that every intersection point x ∈ Tα∩ Tβ consists of an u”
On the wrapped Fukaya category and based loops (2009, methodology): “The exactness condition excludes bubbling of holomorphic discs; a general Lagrangian Floer theory is developed by Fukaya, Oh, Ohta and Ono in [13], but a wrapped version of their theory has not been worked out.”
Disk enumeration on the quintic 3-fold (2006, background): “However, a symplectic invariant via disk enumeration is not defined in [ 3 ].”
On the Fukaya category of a Fano hypersurface in projective space (2013, background): “nding cochains and the disk potential. In Sections 4 (algebra) and 5 (geometry), we explain how to formally enlarge the monotone Fukaya category by including weak bounding cochains, closely following [24]. The rst technical issue to confront is that, in order for weak bounding cochains to make sense”
Spectral numbers in Floer theories (2007, background): “nerated over K. For v ∈ V≥0, let ˜v ∈ V˜ denote the image of v under the quotient map V≥0 → V˜. Our ﬁrst application of Lemma 2.1 is the following, which in retrospect is analogous to Lemma A.4.11 in [5]. Lemma 2.3. If V ≤ ΛK(G)n and u1,...,uk ∈ V≥0 are such that V˜ = spanK{˜u1,..., ˜uk}, then V≥0 =”
Symplectic cohomology and duality for the wrapped Fukaya category (2013, methodology): “Let us also for a moment reason using the conceptually intuitive singular chain variant of Floer theory as developed by [FOOO1].”
Polyfold and Fredholm Theory (2014, background): “There is, of course, a large literature on Gromov-Witten invariants and further developments, see [13, 14, 35, 36, 48, 49, 52, 39, 40, 41, 42].”