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Corrigendum of "Construction of Kuranishi structures on the moduli spaces of pseudo holomorphic disks I, Surveys in Differential Geometry XXII (2018), 133-190"

Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta, Kaoru Ono

Abstract

This is a corrigendum of Lemma 9.1 of the paper [FOOO3] in the title. This lemma is not correct as pointed out by A. Daemi and a referee of the paper [DF]. The corrigendum does not affect the applications of this lemma in [FOOO3] and other papers and exactly the same proofs as therein apply if one replaces the statement of [FOOO3,Lemma 9.1] by Lemma 2 of the present note.

Corrigendum of "Construction of Kuranishi structures on the moduli spaces of pseudo holomorphic disks I, Surveys in Differential Geometry XXII (2018), 133-190"

Abstract

This is a corrigendum of Lemma 9.1 of the paper [FOOO3] in the title. This lemma is not correct as pointed out by A. Daemi and a referee of the paper [DF]. The corrigendum does not affect the applications of this lemma in [FOOO3] and other papers and exactly the same proofs as therein apply if one replaces the statement of [FOOO3,Lemma 9.1] by Lemma 2 of the present note.
Paper Structure (2 sections, 1 theorem, 22 equations)

This paper contains 2 sections, 1 theorem, 22 equations.

Table of Contents

  1. Overview of the corrigendum
  2. Double log smooth structure of $\mathcal{M}^{\rm d}_{k+1,\ell}$

Key Result

Lemma 2

There exists a unique structure of smooth manifold with corners on $\mathcal{M}^{\rm d}_{k+1,\ell}$ such that $\Psi_{s,\phi}$ is a diffeomorphism onto its image for each ${\bf p} \in \mathcal{M}^{\rm d}_{k+1,\ell}$.And for any analytic family of coordinates of the nodal points which is used to defin

Theorems & Definitions (5)

  • Remark 1
  • Lemma 2: Double log smooth structure
  • Remark 3
  • Remark 4
  • proof : Proof of Lemma \ref{['lem91']}