From Good Coordinate Systems to Kuranishi Structures and Back with CF-Perturbations
As we explained at the end of Chap. 4 , it is more canonical to define the notion of fiber products of spaces with Kuranishi structure than to define that of fiber products of spaces with a good coordinate system. On the other hand, in Chap. 7 , we gave
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Kenji Fukaya Yong-Geun Oh Hiroshi Ohta Kaoru Ono
Kuranishi Structures and Virtual Fundamental Chains
Springer Monographs in Mathematics Editors-in-Chief Isabelle Gallagher, Paris, France Minhyong Kim, Coventry UK and Seoul, South Korea Series Editors Sheldon Axler, San Francisco, USA Mark Braverman, Princeton, USA Maria Chudnovsky, Princeton, USA Tadahisa Funaki, Tokyo, Japan Sinan C. Güntürk, New York, USA Claude Le Bris, Marne la Vallée, France Pascal Massart, Orsay, France Alberto A. Pinto, Porto, Portugal Gabriella Pinzari, Padova, Italy Ken Ribet, Berkeley, USA René Schilling, Dresden, Germany Panagiotis Souganidis, Chicago, USA Endre Süli, Oxford, UK Shmuel Weinberger, Chicago, USA Boris Zilber, Oxford, UK
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Kenji Fukaya • Yong-Geun Oh • Hiroshi Ohta Kaoru Ono
Kuranishi Structures and Virtual Fundamental Chains
Kenji Fukaya Simons Center for Geometry and Physics State University of New York Stony Brook, NY, USA Hiroshi Ohta Graduate School of Mathematics Nagoya University Nagoya, Japan
Yong-Geun Oh IBS Center for Geometry and Physics Pohang, Gyung-Buk, Korea Department of Mathematics, Postech Pohang, Gyung-Buk, Korea Kaoru Ono Research Institute for Mathematical Sciences Kyoto University Kyoto, Japan
ISSN 1439-7382 ISSN 2196-9922 (electronic) Springer Monographs in Mathematics ISBN 978-981-15-5561-9 ISBN 978-981-15-5562-6 (eBook) https://doi.org/10.1007/978-981-15-5562-6 Mathematics Subject Classification: Primary 18G70, 53D37, 53D40, 53D45, 57N75, 57R18, 58D27; Secondary 14A20, 37J05, 53D42, 57N65, 57N80, 58C35 © Springer Nature Singapore Pte Ltd. 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors a
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