Director OH Yong-Geun from IBS Center for Geometry and Physics Published a New Book on Kuranishi Structure

Director OH Yong-Geun’s new book, 『Kuranishi Structure and Virtual Fundamental Chains』 has been recently published by Springer, an esteemed publisher of many peer-reviewed journals including Nature. The new book was co-authored by OH Yong-Geun (Institute for Basic Science & POSTECH), Kenji FUKAYA (Simons Center for Geometry and Physics & Stony Brook University), Hiroshi OHTA (Nagoya University), Kaoru ONO (Research Institute for Mathematical Sciences & Kyoto University) as a series of Springer Monographs in Mathematics.

This book lays the foundation of the Kuranishi structure. Director OH explained, “The structure is needed to implement the study of the moduli space of pseudo-holomorphic curves into the construction of A_∞ structures associated with general Lagrangian submanifolds and their deformation theory. The book is expected to be useful in other moduli problems that arise from geometry and physics beyond pseudo-holomorphic curves.”

The package of Gromov’s pseudo-holomorphic curves is a major tool in global symplectic geometry and its applications, including Gromov-Witten invariants, mirror symmetry and Hamiltonian dynamics, as well as being the mathematical representation of open-closed type IIA string theory. The Kuranishi structure was introduced in 1999 by two of the authors of the present volume, Kenji Fukaya and Kaoru Ohno, to apply this machinery on general symplectic manifolds without assuming any specific restrictions. The topic was further expanded by this book’s authors in their monograph 『Lagrangian Intersection Floer Theory』 as well as numerous other publications on the topic that are written by themselves and others.

Director OH said, “We now present this book, in order to answer the popular demand for a detailed, self-contained explanation of the theory of Kuranishi structures, which can be extended to other moduli problems in geometry and physics. We hope that this book can serve as a valuable tool for other mathematicians in the related fields.” The book has been published on November 2020, and it can be purchased from various online platforms including Amazon.