Compactness for punctured holomorphic curves

By Kai Cieliebak, Klaus Mohnke. 2005

96 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ade5ad58424dd876125c7bf3b06f29376d7293c6

How researchers see this paper

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

In Geometry and Topology

1. Michael Hutchings
2. Chris Wendl
3. P. Ghiggini
4. Clifford H. Taubes
5. A. Oancea
6. K. Honda
7. V. Colin
8. Kai Cieliebak

In Mathematical Physics

1. Michael Hutchings
2. Chris Wendl
3. A. Oancea
4. Clifford H. Taubes
5. K. Honda
6. P. Ghiggini
7. Andrew Cotton-Clay
8. V. Colin

Citations in the corpus

• Gluing pseudoholomorphic curves along branched covered cylinders II (2007, background): “Note that the definition of #G(U+, U−) does not count boundary points of the compactification of the moduli space M(α+, α−)/R as in [1, 3] (for all we know there could be infinitely many such boundary points), but rather counts boundary points of a truncation of the moduli space.”
• Weak Symplectic Fillings and Holomorphic Curves (2010, background): “{manifold Mwith stable Hamiltonian structure (; ), the 2{form (2.2) !:= + d(t) on ( ";") M is symplectic for suciently small ">0. Conversely, and more generally (cf. Lemma 2.3 in [CM05]): Lemma 2.3. Let (W;!) be a symplectic 4{manifold whose interior contains a closed oriented hype”
• First steps in stable Hamiltonian topology (2010, background): “Later, they attained importance as the structure on a manifold needed for the compactness result in symplectic field theory [20, 7, 15].”
• Punctured holomorphic curves and Lagrangian embeddings (2014, background): “In this section we recall the definitions and basic properties of punctured holomorphic curves, see [25, 10, 17] for details.”
• The embedded contact homology index revisited (2008, methodology): “We will not really use the symplectic form on X in the present paper, but it enables compactness results for holomorphic curves [1, 3].”
• Symplectic homology and the Eilenberg-Steenrod axioms (2015, methodology): “Since ψ(a) ≥ 0 and ψ(a) ≥ e, and ψ was arbitrary with the given boundary conditions, this yields a uniform bound (independent of R) on the Hofer energy of (a, f) (see [14, 30]).”
• Symplectic Floer homology of area-preserving surface diffeomorphisms (2008, background): “[CM] K. Cieliebak and K. Mohnke.”
• Sutures and contact homology I (2010, methodology): “[BM] F. Bourgeois and K. Mohnke,Coherent orientations in symplectic field theory, Math.”