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

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...

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Κύριος συγγραφέας: Mescher, Stephan (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2018.
Έκδοση:1st ed. 2018.
Σειρά:Atlantis Studies in Dynamical Systems ; 6
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
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245 1 0 |a Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology  |h [electronic resource] /  |c by Stephan Mescher. 
250 |a 1st ed. 2018. 
264 1 |a Cham :  |b Springer International Publishing :  |b Imprint: Springer,  |c 2018. 
300 |a XXV, 171 p. 20 illus.  |b online resource. 
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490 1 |a Atlantis Studies in Dynamical Systems ;  |v 6 
505 0 |a 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. 
520 |a 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. 
650 0 |a Global analysis (Mathematics). 
650 0 |a Manifolds (Mathematics). 
650 0 |a Dynamics. 
650 0 |a Ergodic theory. 
650 0 |a Complex manifolds. 
650 1 4 |a Global Analysis and Analysis on Manifolds.  |0 http://scigraph.springernature.com/things/product-market-codes/M12082 
650 2 4 |a Dynamical Systems and Ergodic Theory.  |0 http://scigraph.springernature.com/things/product-market-codes/M1204X 
650 2 4 |a Manifolds and Cell Complexes (incl. Diff.Topology).  |0 http://scigraph.springernature.com/things/product-market-codes/M28027 
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