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A festschrift to honour Mel Greenhut, who has long toiled on
spatial economics, this book focuses on a single question - if and
how economic space matters, discussing theoretical, as well as
historical issues of contemporary relevance.;Subjects covered
include historical accounts of spatial economics; land use and
public goods; and location theory and spatial competition. Hiroshi
Ohta is the author of "Theory of Spatial Pricing and Market Areas"
(with M.L. Greenhut), "Spatial Price Theory of Imperfect
Competition" and "New Frontiers in Regional Science".
Jacques-Francois Thisse is the co-author of "Discrete Choice Theory
of Product Differentiation".;The contributors include Simon P.
Anderson, William J. Baumol, Bruce L. Benson, Andre de Palma, B.
Curtis Easton, Nicholas S. Economides, Robert B. Ekelund Jr, Ronald
D. Fischer, John G. Greenhut, Timothy J. Gronberg, Robert E.
Hebert, Hong Hwang, Amoz Kats, Tatsuhiko Kawashima, Chao-Cheng Mai,
Milton H. Marquis, Edwin S. Mills, Gordon M. Myers, Hisao Nishioka,
George Norman, Yorgos Y. Papageorgiou, Louis Phlips, Susan
Rose-Ackerman, Noboru Sakashita, Paul A. Samuelson, Douglas G.
Sauer, Thomas R. Saving, Nicolas Schmitt, Takaaki Takaha
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 is a Festschrift to honour Professor Melvin Greenhut who has
long toiled on spatial economics. The book accordingly focuses on a
single question: in what sense 'economic space' matters in economic
theory. Space in economics is an elusive concept, apparently
separating and embracing economic agents at the same time. This is
why adding it to already overly complicated economic agents at the
same time. This is why adding it to already overly complicated
economic models may not necessarily help economics to become
sufficiently realistic. In this book, leading scholars of
international stature try to find ways of introducing space in
economic theory which will make it simpler and more realistic,
analysing theoretical and historical issues of contemporary
relevance, such as land use, congestion and public goods, location
theory and spatial competition.
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.
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