| 书目名称 | Perturbed Gradient Flow Trees and A∞-algebra Structures in Morse Cohomology |
| 编辑 | Stephan Mescher |
| 视频video | |
| 概述 | Introduces a self-contained discussion of an aspect of Morse theory that has remained largely overlooked.Includes an accessible introduction to a part of Morse theory that is closely related to algebr |
| 丛书名称 | Atlantis Studies in Dynamical Systems |
| 图书封面 |  |
| 描述 | 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.. |
| 出版日期 | Book 2018 |
| 关键词 | Morse theory; Morse homology; Geometric topology; A-infinity-algebras; Differential topology |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-319-76584-6 |
| isbn_softcover | 978-3-030-09526-0 |
| isbn_ebook | 978-3-319-76584-6Series ISSN 2213-3526 Series E-ISSN 2213-3534 |
| issn_series | 2213-3526 |
| copyright | Springer International Publishing AG, part of Springer Nature 2018 |
发表于 2025-3-21 16:39:04
