The package of Gromov's pseudo-holomorphic curves is a major tool in global symplectic geometry and its applications, including mirror symmetry and Hamiltonian dynamics. The Kuranishi structure was introduced by two of the authors of the present volume in the mid-1990s to apply this machinery on general symplectic manifolds without assuming any specific restrictions. It was further amplified by this book's authors in their monograph Lagrangian Intersection Floer Theory and in many other publications of theirs and others. Answering popular demand, the authors now present the current book, in which they provide a detailed, self-contained explanation of the theory of Kuranishi structures.
Part I discusses the theory on a single space equipped with Kuranishi structure, called a K-space, and its relevant basic package. First, the definition of a K-space and maps to the standard manifold are provided. Definitions are given for fiber products, differential forms, partitions of unity, and the notion of CF-perturbations on the K-space. Then, using CF-perturbations, the authors define the integration on K-space and the push-forward of differential forms, and generalize Stokes' formula and Fubini's theorem in this framework. Also, "virtual fundamental class" is defined, and its cobordism invariance is proved.
Part II discusses the (compatible) system of K-spaces and the process of going from "geometry" to "homological algebra". Thorough explanations of the extension of given perturbations on the boundary to the interior are presented. Also explained is the process of taking the "homotopy limit" needed to handle a system of infinitely many moduli spaces. Having in mind the future application of these chain level constructions beyond those already known, an axiomatic approach is taken by listing the properties of the system of the relevant moduli spaces and then a self-contained account of the construction of the associated algebraic structures is given. This axiomatic approach makes the exposition contained here independent of previously published construction of relevant structures.
This book reappraises the Japanese employment system, characterized by such practices as the periodic recruiting of new graduates, lifetime employment and seniority-based wages, which were praised as sources of high productivity and flexibility for Japanese firms during the period of high economic growth from the middle of the 1950s until the burst of bubbles in the early 1990s. The prolonged stagnation after the bubble burst induced an increasing number of people to criticize the Japanese employment system as a barrier to the structural changes needed to allow the economy to adjust to the new environment, with detractors suggesting that such a system only serves to protect the vested interests of incumbent workers and firms. By investigating what caused the long stagnation of the Japanese economy, this book examines the validity of this currently dominant view about the Japanese employment system. The rigorous theoretical and empirical analyses presented in this book provide readers with deep insights into the nature of the current Japanese labor market and its macroeconomic impacts.