Existence of a somewhere injective pseudo-holomorphic disc

By L. Lazzarini. 2000

100 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/55e79e4948be93a4df0f5303145debe64a1b6189

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. M. Abouzaid
2. Urs Frauenfelder
3. I. Smith
4. P. Seidel
5. O. Cornea
6. P. Biran
7. Renato Vianna
8. Nick Sheridan

In Geometry and Topology

1. I. Smith
2. M. Abouzaid
3. P. Seidel
4. Nick Sheridan
5. Alexander F. Ritter
6. D. Auroux
7. O. Cornea
8. A. Oancea

Citations in the corpus

• Lagrangian non-intersections (2004, methodology): “[25] L. Lazzarini.”
• The monotone wrapped Fukaya category and the open-closed string map (2012, background): “By Lazzarini [28], for any holomorphic disc u : (D, ∂D) → (X,L), where X is a smooth almost complex manifold and L is a totally real submanifold, there is an underlying simple holomorphic disc v : (D, ∂D)→ (X,L) with image contained in u(D), and the relative homology class [u] ∈ H2(X,L) is a linear ”
• Lagrangian matching invariants for fibred four-manifolds: I (2006, unknown): “One can, how ever, use Lazzarini’s lemma [20]: if δ is a non-constant J–disc then there is a simple J–disc δ′ such that δ′(∂D̄) ⊂ δ(∂D̄).”
• Gromov convergence of pseudoholomorphic disks (2008, background): “For example, Jholomorphic disks play a crucial role in Floer homology for Lagrangian intersections and hence in the proof of the Arnold conjecture (see [Fl], [Oh], [FOOO], [ La ], [Ch]).”
• Rigidity and uniruling for Lagrangian submanifolds (2008, methodology): “1 (Decomposition of disks [37; 38]) Let uW .”
• Homological mirror symmetry for the quartic surface (2003, background): “L) vanishes, and the virtual dimension is (8.15) 2 +µ(w) −3 = −1. Again, this shows that for generic J, there are no somewhere injective discs. The decomposition theorem of Kwon-Oh [36] and Lazzarini [37] says that if there is a non-constant J-holomorphic disc, there is also a somewhere injective on”
• On the Fukaya category of a Fano hypersurface in projective space (2013, background): “It follows from [27, 22] that any JL-holomorphic disk u with boundary on L contains a somewhere-injective JL-holomorphic disk v with boundary on L in its image.”
• Infinitely many monotone Lagrangian tori in del Pezzo surfaces (2016, methodology): “ks with boundary in a monotone Lagrangian Land relative homotopy class is an invariant of the symplectomorphism class of L, rst pointed out in [EP] (we believe that the formal proof needs the work of [Laz]). To distinguish the monotone Lagrangian tori we built in CP2, we used an invariant among mono”
• Framed bordism and Lagrangian embeddings of exotic spheres (2008, background): “ABOUZAID Since β is not divisible, all holomorphic discs in class β are necessarily simple (see [13,18]).”
• Quantum Structures for Lagrangian Submanifolds (2007, methodology): “Below we shall follow Lazzarini’s approach.”