Construction of Kuranishi structures on the moduli spaces of pseudo holomorphic disks: I

Abstract

This is the first of two articles in which we provide detailed and self-contained account of the construction of a system of Kuranishi structures on the moduli spaces of pseudo holomorphic disks, using the exponential decay estimate given in [FOOO7]. This article completes the construction of a Kuranishi structure of a single moduli space. This article is an improved version of [FOOO4, Part 4] and its mathematical content is taken from our earlier writing [FOn,FOOO2,FOOO4,FOOO7]. The version 2 contains a correction of typological errors in the statement of Lemma 10.11 and the statement of Proposition 10.4. The proof of them are not changed. (Note these places were written in the same way as version 1 in the version published in Surveys in Differential Geometry.)

50 pages 3 figures

References in corpus (4)

• Technical details on Kuranishi structure and virtual fundamental chain
• Kuranishi structure, Pseudo-holomorphic curve, and Virtual fundamental chain: Part 1
• Unobstructed Immersed Lagrangian Correspondence and Filtered $A_{\infty }$ Functor
• Kuranishi structure, Pseudo-holomorphic curve, and virtual fundamental chain: Part 2

Cited by in corpus (3)

• Family Floer program and non-archimedean SYZ mirror construction
• Lie groupoid, deformation of unstable curve, and construction of equivariant Kuranishi charts
• Monotone Lagrangian Floer theory in smooth divisor complements: I