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 A8-algebra by means of perturbed gradient flow trajectories. This approach is a variation on K. Fukaya’s definition of Morse-A8-categories for closed oriented manifolds involving families of Morse functions. To make A8-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.
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.
Produkteigenschaften
- Artikelnummer: 9783030095260
- Medium: Buch
- ISBN: 978-3-030-09526-0
- Verlag: Springer International Publishing
- Erscheinungstermin: 19.12.2018
- Sprache(n): Englisch
- Auflage: Softcover Nachdruck of the original 1. Auflage 2018
- Serie: Atlantis Studies in Dynamical Systems
- Produktform: Kartoniert, Paperback
- Gewicht: 312 g
- Seiten: 171
- Format (B x H x T): 155 x 235 x 12 mm
- Ausgabetyp: Kein, Unbekannt