Perturbed Gradient Flow Trees and A8-algebra Structures in Morse Cohomology
Softcover Reprint of the Original 1st 2018 ed.
Book Details
Format
Paperback / Softback
Book Series
Atlantis Studies in Dynamical Systems
ISBN-10
3030095266
ISBN-13
9783030095260
Edition
Softcover Reprint of the Original 1st 2018 ed.
Publisher
Springer Nature Switzerland AG
Imprint
Springer Nature Switzerland AG
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Dec 19th, 2018
Print length
171 Pages
Ksh 9,900.00
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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.
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.
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