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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| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cham :
Springer International Publishing,
2018.
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| Ausgabe: | 1st ed. 2018. |
| Schriftenreihe: | Atlantis Studies in Dynamical Systems ;
6 |
| Schlagworte: | |
| ISBN: | 9783319765846 |
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| 020 | |a 9783319765846 | ||
| 024 | 7 | |a 10.1007/978-3-319-76584-6 |2 doi | |
| 035 | |a CVTIDW12590 | ||
| 040 | |a Springer-Nature |b eng |c CVTISR |e AACR2 | ||
| 041 | |a eng | ||
| 100 | 1 | |a Mescher, Stephan. |4 aut | |
| 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. | ||
| 260 | 1 | |a Cham : |b Springer International Publishing, |c 2018. | |
| 300 | |a XXV, 171 p. 20 illus. |b online resource. | ||
| 490 | 1 | |a Atlantis Studies in Dynamical Systems ; |v 6 | |
| 500 | |a Mathematics and Statistics | ||
| 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. | |
| 516 | |a text file PDF | ||
| 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. | |
| 856 | 4 | 0 | |u http://hanproxy.cvtisr.sk/han/cvti-ebook-springer-eisbn-978-3-319-76584-6 |y Vzdialený prístup pre registrovaných používateľov |
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| 919 | |a 978-3-319-76584-6 | ||
| 974 | |a andrea.lebedova |f Elektronické zdroje | ||
| 992 | |a SUD | ||
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