| 书目名称 | Morse Theory and Floer Homology |
| 编辑 | Michèle Audin,Mihai Damian |
| 视频video | |
| 概述 | Translation of the popular French textbook.Provides a unified presentation of Morse theory and Floer homology that is unique in the English language.Explains all the required background on symplectic |
| 丛书名称 | Universitext |
| 图书封面 |  |
| 描述 | .This book is an introduction to modern methods of symplectic topology. It is devoted to explaining the solution of an important problem originating from classical mechanics: the ‘Arnold conjecture‘, which asserts that the number of 1-periodic trajectories of a non-degenerate Hamiltonian system is bounded below by the dimension of the homology of the underlying manifold..The first part is a thorough introduction to Morse theory, a fundamental tool of differential topology. It defines the Morse complex and the Morse homology, and develops some of their applications..Morse homology also serves a simple model for Floer homology, which is covered in the second part. Floer homology is an infinite-dimensional analogue of Morse homology. Its involvement has been crucial in the recent achievements in symplectic geometry and in particular in the proof of the Arnold conjecture. The building blocks of Floer homology are more intricate and imply the use of more sophisticated analytical methods, all of which are explained in this second part..The three appendices present a few prerequisites in differential geometry, algebraic topology and analysis..The book originated in a graduate course given |
| 出版日期 | Textbook 2014 |
| 关键词 | Arnold Conjecture; Floer Complex; Floer Homology; Gluing; Hamiltonian System; Maslov Index; Morse Complex; |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-1-4471-5496-9 |
| isbn_softcover | 978-1-4471-5495-2 |
| isbn_ebook | 978-1-4471-5496-9Series ISSN 0172-5939 Series E-ISSN 2191-6675 |
| issn_series | 0172-5939 |
| copyright | Springer-Verlag London Ltd., part of Springer Nature 2014 |
发表于 2025-3-21 16:28:10
