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＜電子ブック＞
Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology / by Stephan Mescher
(Atlantis Studies in Dynamical Systems. ISSN:22133534 ; 6)

版	1st ed. 2018.
出版者	Cham : Springer International Publishing : Imprint: Springer
出版年	2018
大きさ	XXV, 171 p. 20 illus : online resource
著者標目	*Mescher, Stephan author SpringerLink (Online service)
件　名	LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Dynamical systems FREE:Global Analysis and Analysis on Manifolds FREE:Dynamical Systems FREE:Manifolds and Cell Complexes
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-76584-6

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