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Titlebook: Kuranishi Structures and Virtual Fundamental Chains; Kenji Fukaya,Yong-Geun Oh,Kaoru Ono Book 2020 Springer Nature Singapore Pte Ltd. 2020

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Introduction,e a differential geometric foundation on the study of moduli spaces of pseudo-holomorphic curves entering on the one hand in the Gromov–Witten theory and on the other in the study of the Arnold conjecture in symplectic geometry . on general compact symplectic manifolds.
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CF-Perturbations and Integration Along the Fiber (Pushout)uct of other members. We will obtain an algebraic structure on certain cochain complexes which realize the homology groups of certain spaces. They are the spaces over which we take fiber products between members of the system of K-spaces.
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Zero-and One-Dimensional Cases via Multivalued Perturbationis chapter, we discuss another method based on multivalued perturbations. Here we restrict ourselves to the case when the dimension of K-spaces of our interest is 1, 0 or negative, and define a virtual fundamental chain over . in the 0-dimensional case. In spite of this restriction, the argument of
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Kenji Fukaya,Yong-Geun Oh,Hiroshi Ohta,Kaoru Onorgy into mechanical energy with a three-dimensional network of cross-linked filament molecules..Several high polymer systems are discussed:.Investigations of the Donnan-equilibrium between the gel and embedding-fluid show theoretically and experimentally that stretching of the p.-muscle is associate
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Kenji Fukaya,Yong-Geun Oh,Hiroshi Ohta,Kaoru Onorgy into mechanical energy with a three-dimensional network of cross-linked filament molecules..Several high polymer systems are discussed:.Investigations of the Donnan-equilibrium between the gel and embedding-fluid show theoretically and experimentally that stretching of the p.-muscle is associate
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