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# Surveys in Differential Geometry

## Volume 22 (2017)

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

Pages: 133 – 190

DOI: http://dx.doi.org/10.4310/SDG.2017.v22.n1.a6

#### Authors

#### 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].

Kenji Fukaya is supported partially by NSF Grant No. 1406423 and Simons Collaboration on homological Mirror symmetry, Yong-Geun Oh by the IBS project IBS-R003-D1, Hiroshi Ohta by JSPS Grant-in-Aid for Scientific Research No. 15H02054 and Kaoru Ono by JSPS Grant-in-Aid for Scientific Research, Nos. 21244002, 26247006.

Published 13 September 2018