Symplectic topology on subcritical manifolds

By P. Biran, Kai Cieliebak. 2001

94 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/42237fe12479fc9932498bd9ed096f7626d7952e

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Citations in the corpus

Rigid subsets of symplectic manifolds (2007, background): “on that, in particular, the special ﬁber is non-empty and so pspec ∈ ∆. Moreover pspec is an interior point of ∆ – otherwise Φ−1(pspec) is isotropic of dimension <nand hence displaceable (see e.g. [10]). Remark 1.8. If dimM= 2dimTk (that is we deal with the symplectic toric manifold), the special”
The Gromov width of 4-dimensional tori (2011, background): “Computations and estimates of the Gromov width for various examples can be found in [4, 5, 6, 15, 18, 19, 21, 22, 29, 34, 38, 41, 42].”
On the extrinsic topology of Lagrangian submanifolds (2005, background): “l Maslov number is necessary, since otherwise the Lagrangian submanifold might be displaceable. Indeed, there exist displaceable Lagrangian spheres Lin symplectic manifolds of the form Xn+1 ×CPn, cf. [3]. Since L is simply connected it is monotone and NL = dimL+ 1. Furthermore, an analogous calculat”
Lagrangian spheres, symplectic surfaces and the symplectic mapping class group (2010, unknown): “1 in [9] and Lemma 6 in [52], (U0, J0, φh) is a complete Stein manifold of finite type with Kähler form ωh = −d(dφh ◦ J0).”
Quasi-states and symplectic intersections (2004, unknown): “[12]).”
Lagrangian non-intersections (2004, background): “Indeed, for any symplectic manifold X of dimC X = n + 1, CP n × X has a Lagrangian sphere, after a possible rescaling of the symplectic form on the X factor (see [9] for details).”
Floer cohomology and disc instantons of Lagrangian torus fibers in Fano toric manifolds (2003, unknown): “o its deﬁnition has been developed by Fukaya-Oh-OhtaOno [FOOO]. It has been proven to be a powerful tool in studying various problems in symplectic geometry (see [Fl], [O4], [Che], [P], [Se], [FOOO], [BC], and [TY], for example). The theory itself was greatly enhanced by the advent of the Fukaya cat”
Floer homology on the universal cover, a proof of Audin's conjecture and other constraints on Lagrangian submanifolds (2010, background): “These manifolds were studied in [7] by P.”
Rigidity and uniruling for Lagrangian submanifolds (2008, background): “If L is narrow, as L cannot be a homology sphere (see eg Biran and Cieliebak [9]) we can take l D n 1 in Theorem 1.”
Introduction to Symplectic Field Theory (2000, background): “of the function φ, which is automaticallyisotropicfor the symplectic form ω(see [14]), and, in particular, dimK ≤n. Biran-Cieliebak call the pair (W,W 0) subcritical if dimK<n. They constructed in [6] several interesting examples of subcritical pairs, and conjectured that if (W,W 0) is subcritica”
Symplectic mapping class groups of some Stein and rational surfaces (2009, methodology): “ There is also a standard construction given a (possibly incomplete) ﬁnite-type Stein manifold (W,J,φ) to obtain a complete ﬁnite-type Stein manifold. Let h denote the function h(x) = ex−1. Lemma 10 ([BC01], lemma 3.1 and [SS05] lemma 6). Deﬁne φh:= h◦φ. (W,J,φh) is a complete Stein manifold of ﬁnit”
Quantitative symplectic geometry (2005, unknown): “Since then, lots of new capacities have been defined [16, 30, 32, 44, 49, 59, 60, 90, 99] and they were further studied in [1, 2, 8, 9, 17, 26, 21, 28, 31, 35, 37, 38, 41, 42, 43, 46, 48, 50, 52, 56, 57, 58, 61, 62, 63, 64, 65, 66, 68, 74, 75, 76, 88, 89, 91, 92, 94, 97, 98].”