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

摘要

The purpose of this erratum is to correct a number of inconsistencies in our paper [1]. These are related to the grading of generalized Floer homology and do not affect formulations and proofs of the main results of the paper. The source of the mistakes in the grading is as follows. Consider the framed Hamiltonian structure (V velence M X S~(1), THETA velence -alpha + H_(t)dt, lambda velence dt) associated to a Hamiltonian function H: M X S~(1) -> R on an exact symplectic manifold (M, omega velence d(alpha)), as in Example 4.2.2. The symplectic form OMEGA velence d(THETA) on the cut of this Hamiltonian structure equals the form -omega (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.