Erratum to “Geometry of contact transformations and domains: orderability versus squeezing”

By Y. Eliashberg, Sang Seon Kim, L. Polterovich. 2005

178 citations recorded by the source corpus.

associated to a Hamiltonian function H WM S!R on an exact symplectic manifold .M; ! D d /, as in Example 4.2.2. The symplectic form D d‚ on the cut of this Hamiltonian structure equals the form ! (mind the minus sign). In the proof of Proposition 4.37 we claim that “the change of the sign of the symplectic form does not affect Conley–Zehnder indices”, which is wrong for the definition of Conley–Zehnder indices as presented in Section 4.4.1. In order to correct this, the following changes should be made in paper:

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Citations in the corpus

Sheaf quantization of Hamiltonian isotopies and applications to non displaceability problems (2010, background): “The following definition is due to [7] and is used in [4, 5] where the authors prove Corollary 4.”
Relative asymptotic behavior of pseudoholomorphic half‐cylinders (2007, background): “For examples of framed stable Hamiltonian structures see [1] or [4].”
Geometric criteria for overtwistedness (2015, background): “1, being a contact squeezing result, relates to non–orderability [4, 13, 20, 32].”
Existence and classification of overtwisted contact structures in all dimensions (2014, background): “in the case of RP 2n−1 (see [26]) or the unit cotangent bundle UT ∗(M) of a closed manifold M , see [17, 9].”
Brieskorn manifolds in contact topology (2013, background): “by the following rule. For f;~ ~g 2Cont^ 0( ;˘), we say that f~ g~ if f~~g 1 is represented by a path that is generated by non-negative contact Hamiltonians. The notion of orderability was dened in [EKP]. Denition 6.1 (Eliashberg-Kim-Polterovich). We call a contact manifold ( ;˘= ker) orderable if d”
Intersection theory of punctured pseudoholomorphic curves (2009, background): “Following [5], we will refer to a pair H = (λ, ω) satisfying (H1)– (H3) as a stable Hamiltonian structure on M .”
First steps in stable Hamiltonian topology (2010, result): “Stable Hamiltonian structures also appear in work of Eliashberg, Kim and Polterovich [21] and Wendl [44].”
Automatic transversality and orbifolds of punctured holomorphic curves in dimension four (2008, background): “purposes. The data (�,X,!) are equivalent to the definition of a framed Hamiltonian structure stated in [ EKP06 ], with the exception that the latter requires ! to be exact; here it need only be closed.”
The homology of path spaces and Floer homology with conormal boundary conditions (2008, unknown): “This approach is taken in the context of generalized Floer homology in [6].”
Boundary depth in Floer theory and its applications to Hamiltonian dynamics and coisotropic submanifolds (2009, unknown): “, [7]) to the existence of α ∈ Ω(1)(N) such that α ∧ (ω|N ) n−1 is a volume form and ker dα ⊂ kerω|N ; for one direction, given ψ : (−ǫ, ǫ) × N → M inducing the same characteristic foliation on each {t} ×N , we can recover α by writing ψω = dt ∧ αt + ωt where αt ∈ Ω (1)(N) and ωt ∈ Ω (2)(N), for the”