Document Type
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BL
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Record Number
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865179
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Main Entry
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Mescher, Stephan.
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Title & Author
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Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology\ by Stephan Mescher.
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Publication Statement
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Cham :: Springer International Publishing :: Imprint :: Springer,, 2018.
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Series Statement
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Atlantis Studies in Dynamical Systems ;; 6
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Page. NO
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1 online resource (XXV, 171 pages 20 illustrations) :: online resource
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ISBN
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3319765833
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: 3319765841
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: 9783319765839
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: 9783319765846
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9783319765839
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Bibliographies/Indexes
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Includes bibliographical references and index.
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Contents
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1. Basics on Morse homology -- 2. Perturbations of gradient flow trajectories -- 3. Nonlocal generalizations -- 4. Moduli spaces of perturbed Morse ribbon trees -- 5. The convergence behaviour of sequences of perturbed Morse ribbon trees -- 6. Higher order multiplications and the A∞-relations -- 7. A∞-bimodule structures on Morse chain complexes -- A. Orientations and sign computations for perturbed Morse ribbon trees.
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Abstract
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This book elaborates on an idea put forward by M. Abouzaid on equipping the Morse cochain complex of a smooth Morse function on a closed oriented manifold with the structure of an A∞-algebra by means of perturbed gradient flow trajectories. This approach is a variation on K. Fukaya's definition of Morse-A∞-categories for closed oriented manifolds involving families of Morse functions. To make A∞-structures in Morse theory accessible to a broader audience, this book provides a coherent and detailed treatment of Abouzaid's approach, including a discussion of all relevant analytic notions and results, requiring only a basic grasp of Morse theory. In particular, no advanced algebra skills are required, and the perturbation theory for Morse trajectories is completely self-contained. In addition to its relevance for finite-dimensional Morse homology, this book may be used as a preparation for the study of Fukaya categories in symplectic geometry. It will be of interest to researchers in mathematics (geometry and topology), and to graduate students in mathematics with a basic command of the Morse theory.
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Subject
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Complex manifolds.
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Subject
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Dynamics.
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Subject
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Ergodic theory.
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Subject
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Global analysis (Mathematics)
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Subject
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Manifolds (Mathematics)
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Subject
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Mathematics.
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Subject
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Complex manifolds.
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Subject
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Dynamics.
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Subject
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Ergodic theory.
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Subject
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Global analysis (Mathematics)
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Subject
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Manifolds (Mathematics)
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Subject
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MATHEMATICS-- Topology.
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Subject
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Mathematics.
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Dewey Classification
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514/.23
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LC Classification
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QA614-614.97
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