Holomorphic Disks and the Chord Conjecture
By Klaus Mohnke. 2000
77 citations recorded by the source corpus.
We prove (a weak version of) Arnold's Chord Conjecture using Gromov's ``classical'' idea in to produce holomorphic disks with boundary on a Lagrangian submanifold.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/4f4eb4d7606c6b9cf5167ccd7497068e2d0e5e61
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In Applied Mathematics
In Geometry and Topology
- Michael Hutchings
- Alexander F. Ritter
- Kai Cieliebak
- Klaus Mohnke
- A. Oancea
- P. Seidel
- Frederick J. Bourgeois III
- Clifford H. Taubes
Citations in the corpus
- Handle attaching in symplectic homology and the Chord Conjecture (2002, unknown): “1 After this paper was submitted, K. Mohnke [ 21 ] independently attacked the Chord”
- Proof of the Arnold chord conjecture in three dimensions, II (2010, unknown): “For the 3-sphere with any contact form inducing the standard contact structure, and more generally for boundaries of subcritical Stein manifolds in any odd dimension, this was proved by Mohnke [11].”
- Taubes’s proof of the Weinstein conjecture in dimension three (2009, background): “This has been proved for the standard contact structure on S(3) [47], and for Legendrian unknots in tight contact 3-manifolds satisfying certain assumptions [1], but it seems that not too much is known about the general case.”
- Topological quantum field theory structure on symplectic cohomology (2010, background): “In this example, the existence of one Reeb chord for any Legendrian K ⊂ ∂M is due to Mohnke [25].”
- Punctured holomorphic curves and Lagrangian embeddings (2014, background): “It was proved by the second author in [50].”