Surveys in Differential Geometry

Volume 22 (2017)

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

Pages: 133 – 190



Kenji Fukaya (Simons Center for Geometry and Physics, State University of New York, Stony Brook, N.Y., U.S.A.)

Yong-Geun Oh (Center for Geometry and Physics, Institute for Basic Sciences (IBS), Pohang, Korea; and Department of Mathematics, POSTECH, Pohang, Korea)

Hiroshi Ohta (Graduate School of Mathematics, Nagoya University, Nagoya, Japan)

Kaoru Ono (Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan)


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].

Full Text (PDF format)

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