Band 6
Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology
Aus der Reihe
Atlantis Studies in Dynamical Systems
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- Hardcover ausgewählt
- Taschenbuch
- eBook
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Sprache:Englisch
Fr. 127.00
inkl. gesetzl. MwSt.,
Beschreibung
Produktdetails
Einband
Gebundene Ausgabe
Erscheinungsdatum
07.05.2018
Abbildungen
XXV, 171 p. 20 illus.
Verlag
SpringerSeitenzahl
171
Maße (L/B/H)
24.1/16/1.7 cm
Gewicht
471 g
Auflage
1st ed. 2018
Sprache
Englisch
ISBN
978-3-319-76583-9
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 beof 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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