Fredholm theory and transversality for noncompact pseudoholomorphic mapsin symplectizations

By D. Dragnev. 2004

113 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8623d3308b4fd2465c97c8b500254676e1a760a1

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Automatic transversality and orbifolds of punctured holomorphic curves in dimension four (2008, background): “the structure of a smooth orbifold of dimension ind(u0;c), with isotropy group Aut(u0) at (j0,u0) and a natural isormorphism T(j 0,u0) (U/G) = kerD∂¯J(j0,u0)/aut(Σ˙,j0). One can adapt the argument in [Dra04] to show that charts constructed in this way are always smoothly compatible. To complete the ”
Erratum to “Geometry of contact transformations and domains: orderability versus squeezing” (2005, background): “The proof of this statement is scattered in the literature for various classes of framed Hamiltonian structures (see eg [31; 14; 5]).”
Rounding corners of polygons and the embedded contact homology of T 3 (2004, methodology): “he relative ﬁrst Chern class with respect to ˝, see our earlier paper [9, Section 2]. The following proposition is the 3–dimensional case of a formula from [7] which is proved in the paper by Dragnev [6], using an index calculation by Schwarz [21]. Proposition 11.2 If J is generic, and if u 2MJ(;) h”
Sutures and contact homology I (2010, background): “In fact, the transversality argument in [9] carries over directly to the sutured case.”
Reeb orbits and the minimal discrepancy of an isolated singularity (2014, methodology): “ation of Jinside some open region U, we have that all smooth somewhere injective J-holomorphic curves with image intersecting Uare regular. We only need such a statement in order to apply a result in [Dra04] inside the proof of Lemma 6.8. We will ﬁrst talk about neck stretching (described in detail ”
Contact homology and homotopy groups of the space of contact structures (2004, background): “Lemma 1 was originally proved by Dragnev [4], and will be proved independently in the Appendix.”
Legendrian ambient surgery and Legendrian contact homology (2012, background): “t; see for example [5, Theorem 2.14] together with [36, Theorem 3.1.6]. However, if one wishes to ﬁnd a regular cylindrical almost complex structure, the argument needs to be reﬁned. This was done in [12] for curves without boundary. This result can be generalised to the moduli spaces under consider”
Weak and strong fillability of higher dimensional contact manifolds (2011, methodology): “Transversality for these curves can therefore be achieved via a generic perturbation of the almost complex structure, using the standard result of Dragnev [12] (see also the appendix of [5]).”
The embedded contact homology index revisited (2008, background): “It is shown in [4], using an index formula from [20], that if J is generic and C is simple, then the moduli space M(α+, α−, [C]) is a manifold near C of dimension ind(C).”
Reeb vector fields and open book decompositions (2008, methodology): “lable. For the asymptotics, refer to Hofer-Wysocki-Zehnder [HWZ1]. Compactness was explainedin [BEHWZ]. The Fredholm theory and transversality (for non-multiply-covered curves)were treated by Dragnev [Dr]. For the Morse-Bott approach, refer to [Bo1]. Examples of contact homology calculations were do”
Intersection theory of punctured pseudoholomorphic curves (2009, background): “This viewpoint is further supported by the fact that considering weighted fredholm theory arguments as in [11, 3], one would expect that the space of pairs of curves (u, v) with δ∞(u, v) > 0 should have positive codimension in the universal moduli space of pseudoholomorphic curves.”
Cylindrical contact homology for dynamically convex contact forms in three dimensions (2014, unknown): “ld cut out transversely. (c) If γ+ and γ− are good, then the function d: MJ 2(γ+,γ−)/R−→ Z >0, which associates to each cylinder its covering multiplicity, is locally constant. Proof. We know from [8] that if Jis generic, then all irreducible somewhere injective J-holomorphic curves are cut out t”
A hierarchy of local symplectic filling obstructions for contact $3$-manifolds (2010, background): “t is nonzero and constant at inﬁnity with respect to Φ. We say that an almost complex structure J∈ J(H) is Fredholm regular if all somewhere injective curves in M(J) are Fredholm regular. As shown in [Dra04] or the appendix of [Bou06], the set of Fredholm regular almost complex structures is of seco”
THE WEINSTEIN CONJECTURE FOR PLANAR CONTACT STRUCTURES IN DIMENSION THREE (2004, unknown): “→ F between Banach spaces. Here E and F are suitable Sobolev completions of the space of sections, respectively (0,1)-forms, in the pullback bundle ˜u∗T(R×M). According to [17] for embeddings ˜u, and [3] in general, the Fredholm index of D is given by (2.5) ind(˜u) = µ(˜u)−2+#Γ. If ˜u is an embeddin”
Lecture Notes on Embedded Contact Homology (2013, background): “1 consists of a tranversality argument in [12] and an index calculation in [50].”