رکورد قبلیرکورد بعدی

" Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology "


Document Type : BL
Record Number : 865179
Main Entry : Mescher, Stephan.
Title & Author : Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology\ by Stephan Mescher.
Publication Statement : Cham :: Springer International Publishing :: Imprint :: Springer,, 2018.
Series Statement : Atlantis Studies in Dynamical Systems ;; 6
Page. NO : 1 online resource (XXV, 171 pages 20 illustrations) :: online resource
ISBN : 3319765833
: : 3319765841
: : 9783319765839
: : 9783319765846
: 9783319765839
Bibliographies/Indexes : Includes bibliographical references and index.
Contents : 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.
Abstract : 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.
Subject : Complex manifolds.
Subject : Dynamics.
Subject : Ergodic theory.
Subject : Global analysis (Mathematics)
Subject : Manifolds (Mathematics)
Subject : Mathematics.
Subject : Complex manifolds.
Subject : Dynamics.
Subject : Ergodic theory.
Subject : Global analysis (Mathematics)
Subject : Manifolds (Mathematics)
Subject : MATHEMATICS-- Topology.
Subject : Mathematics.
Dewey Classification : ‭514/.23‬
LC Classification : ‭QA614-614.97‬
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