| Perturbed Gradient Flow Trees and A∞-Algebra Structures in Morse Cohomology 2018 Edition Contributor(s): Mescher, Stephan (Author) |
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ISBN: 3319765833 ISBN-13: 9783319765839 Publisher: Springer OUR PRICE: $94.99 Product Type: Hardcover - Other Formats Published: May 2018 |
| Additional Information |
| BISAC Categories: - Mathematics | Mathematical Analysis - Mathematics | Topology - General - Science | System Theory |
| Dewey: 514.34 |
| Series: Atlantis Studies in Dynamical Systems |
| Physical Information: 0.5" H x 6.14" W x 9.21" (1.01 lbs) 171 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |
